Captain reported a runway incursion during taxi out at PWM; citing airport signage as contributing.

Narrative

I was operating Aircraft X out of PWM on at approximately XA30Z. We were parked at the gate and had requested push back on ground frequency because we needed clearance to be pushed onto the taxiway. Ground control cleared us for the pushback and we began our push; started the #1 engine and waived the push crew off once disconnected. At this point we discussed changing the departure runway due to the high gusting winds that favored Runway 36 (350 @ 15/ gusts 22). We had initially selected Runway 29 because we had be cleared on the NUBLE4 departure which only allows selection of runways. We then proceeded to do the flight control check and when the First Officer moved the control wheel left and right the inboard aileron control surface boxes were highlighted with yellow X's. We had performed the hydraulic warm-up when getting to the plane because of the low outside air temperature and the hydraulic pumps were in the correct positions. I checked the hydraulic temperatures via the synoptics page and all were showing an adequate temperature and pressure as well. I turned the pumps on for a few minutes to see if that would fix the issue and it did not this first time.At this point Ground control asked if we preferred Runway 36 for departure. We agreed that was the better choice and I requested a new clearance. Ground gave us a clearance of on departure fly runway heading up to 3000 ft; expect to rejoin the NUBLE4 departure at the NUBLE intersection. We then selected Runway 36 in the FMS and we had to input the departure fixes manually because we were unable to select the NUBLE4 when departing 36. We had the FMS updated; received new ACARS takeoff data and had checked/briefed the new clearance/routing. At this point I had let the hydraulic pumps run a little longer because it was so cold out and I knew this would eventually fix our issue. At this point we had been sitting on the taxiway just off the gate for quite some time. Aircraft Y had taxied out and we were blocking them from continuing to Runway 36. Ground asked if we were ready to move because of this and we replied that we had to manually input all the departure fixes and run a checklist and that we were addressing an issue. At this point we had been quite task saturated between the weather updates; the flight control issue; the updated clearance; manual input of departure fixes; sending for and updating ACARS takeoff data; and now being asked to move so Aircraft Y could depart. We still hadn't had a good flight control check but we elected to move out of Aircraft Y's way so they could get on their way. We notified ground that we could move but needed to address an issue still. Ground control instructed us to taxi straight ahead; left on Alpha; and hold short Runway 36 on Alpha and the First Officer read this back. Ground then instructed Aircraft Y to turn left on Charlie and cross Runway 29. We cleared our left and right side and we started to move ahead on Taxiway Charlie and I believe that I briefed the first officer out loud saying left on Alpha to cross 36. At this point he read back the same thing. I misinterpreted Grounds instructions because they had cleared Aircraft Y to cross a runway right after giving us taxi instructions. I had it in my head that they had also instructed us to cross Runway 36 in order to get out of their way because that intersection at Taxiway Alpha and Charlie is a little congested and noted on the chart as Hot Spot 1. We turned onto Alpha and I turned on all the lights and said clear left cleared to cross. The first officer said clear right clear to cross. At this point I had all the momentum I needed to cross the runway and was committed to crossing. We had visually cleared the runway making sure there was no traffic conflict. I had already crossed the 36 hold short line on Taxiway Alpha when ground instructed us to "hold short right there". I hesitated due to the fact that we were already partially on the runway and realized we had notfollowed grounds initial instructions properly. I visually cleared the runway again and elected to fully cross because there was no traffic conflict and I didn't want to stop partially on the runway surface. Ground then said 'anywhere there just stop moving". We then addressed the flight control issue while stopped and successfully completed a flight control check with no further issues. Ground control then got back to us with a possible pilot deviation and gave us a number to call once arriving in ZZZ1. We complied and I briefly asked what our initial instruction was because I obviously interpreted their instructions incorrectly. The controller informed us that he had "just came upstairs so he didn't know how things transpired" and was unaware of the initial instruction. We then received instruction to continue via Alpha and hold short Runway 29. we were then instructed to cross 29 to Alpha; Bravo; hold short 36. we were then instructed to cross 36 at bravo; left Charlie. We then took off on Runway 36 and commenced the rest of the flight uneventfully. I; the Captain take full responsibility and accountability for my actions and mistake in unknowingly starting to cross and fully crossing Runway 36 without proper clearance from ground control.Safety is a big concern of mine while operating an aircraft and unfortunately I didn't perform to my personal standards yesterday. I increased the risk level by not properly confirming our initial taxi instructions. I also failed to write down those taxi instructions. After contemplating and reflecting on the events that occurred yesterday; I have discovered several things that I can improve upon. Firstly; my task management skills. We were heavily task saturated in a short amount of time and I should have taken a pause to fully asses the situation and communicate a plan of action with my first officer. Secondly; my time management. I was feeling slightly rushed with the aircraft waiting for us to move while we still had several tasks to complete. We were safe to move; however; looking back I would've been more assertive in my requests to ATC to find a good spot to move to and hold. ATC did nothing wrong in their instruction but I believe there was maybe a better spot to move to in order to address our situation. I was more concerned with letting Aircraft Y get past us to depart than where I was taxiing to. Thirdly; my taxi brief and confirmation of instructions. We had such a short distance to move and I believe this also played a factor in our mistake. Typically we are used to getting on several taxiways before having to cross a runway. I do not recall if I properly briefed our change in taxi instructions with my first officer. Altogether I have learned a great deal from this mistake and will be more vigilant of my actions moving forward. Especially at airports that I am less familiar with like PWM. One thing I would like to add are some discrepancies on the PWM 10-9 and 10-9C diagrams. While these discrepancies did not dictate the outcome of my mistake I would like to bring them to light for other crews. On the northwest corner of taxiway intersection Alpha and Charlie there is an "Island' with signage that is not properly depicted on either the 10-9 or 10-9C charts. Also; on the 10-9C chart there is a lead-in line to gate off of Taxiway Alpha depicted. This specific line is not depicted on the actual pavement and may cause confusion when attempting to taxi in this area or into gate. Overall; this mistake has resulted in a lot of contemplation on how I can be a better pilot; communicator; and Captain. While not an excuse; I am still learning and adjusting to my new role as Captain. Again; I take full responsibility and accountability for the mistakes that I accidentally made yesterday."