A pilot on short final to a non-towered airport reported a NMAC with an aircraft departing an intersecting runway.

Narrative

Myself and a CFII rated pilot filed IFR flight plan from ZZZ1 to ZZZ. It was briefed that on this leg; I was pilot in command (PIC) and would be under the usage of foggles; while the CFII rated pilot would be the safety pilot and handle all radio calls. The CFII was not acting as CFII; but as a safety pilot. It was CAVU; but we filed anyway to have usage of ATC services and to practice in the system. About 20 miles out of ZZZ; we were having a tough time with ATC transmissions due to the terrain; and were given lower altitude to start our approach. Our primary flight display (PFD) had the latest METAR at ZZZ which had the winds variable at 4 kts.My safety pilot called the field in sight to ATC; at which time they asked if we wanted to cancel IFR and proceed VFR. He canceled for ease of trying to communicate with broken signal approximately 20 miles north of the field.I set up to mirror the RNAV approach to XX; as we were coming from the north and it aligned well. We did not perform the published RNAV as we were visual to Runway XX. The safety pilot called out on Unicom at 20; 15; 10; and 5 miles our intent. We heard other planes in the pattern using Runway XY; and were monitoring their position; but did not have visual contact on any of them. As we were on short final; of about 1 mile; a female pilot inquired about our position; in which the safety pilot said 'on short final; 1 mile out'. I did not hear a clear response; but apparently she said 'I'm going to start my roll on XY'. During this time; I visually obtained the windsock at the end of XX; and confirmed we had chosen the downwind approach correctly.I was focused on the approach and touchdown point at this phase and didn't hear any other radio transmissions; so I assumed she was waiting on our arrival. As I was just about to flare; the safety pilot called out 'my controls' and we successfully transferred flight responsibilities within our airplane. I looked immediately to the left; and saw a Cessna in a climb directly over our wingtip as the safety pilot successfully finished the landing with a firm landing. I estimate we were 300 ft. from the location of the Cessna; and they overflew us by about 200 ft.On a debrief with my safety pilot on the taxi back in; we discussed the radio transmissions between us and the Cessna and what we could have done differently. Even though we thought we were very communicative on call outs during the approach phase; when she announced something we didn't understand; we should have broken off our approach or told her to stop her roll; or both; until the conflict was resolved by both parties. As we continued our taxi back in; we obtained a visual on the other windsock on the field; which was clearly indicating Runway XY would have been preferred; which was in direct conflict as the other windsock at the end of Runway XX.