Air carrier pilot reported temporary loss of aircraft control as the flight went through an area of turbulence and mountain wave. Flight crew regained control after exiting the weather conditions.

Narrative

I was pilot monitoring during these events. We were at FL350 doing .77mach near the frontal range of the Rocky Mountains; close to the DEN airport. We both were aware of weather developing in the area with tops between FL500-600. We saw we needed to deviate around said storms and elected to deviate to the south of course. We deduced it was on the upwind side of the storms; with what appeared to be good separation of storms; and was closer to our original flight plan. Multiple other aircraft had done the same with many going through the same gap in storms; with aircraft going both east and westbound with 1;000 ft of separation between many of them. Prior to getting close to the weather we started to experience light to moderate chop and had our flight attendants take their seats. ATC requested us to climb to FL370 due to heavy traffic and we saw at our weight that we could do so; we then complied and climbed to FL370.As we entered the gap in the weather; I noticed that indeed there were many aircraft in this small area with at least 8 depicted on the Navigation Display (ND); many at or just below our altitude. While holding our speed at .77 we started to experience moderate turbulence with the airplane being buffeted in altitude and rolling. The Autopilot at this time was having trouble with dealing with the turbulence but was keeping up with it. Shortly after we both had noticed our airspeed was decreasing steadily. We both voiced this and I said we had gotten into a mountain wave as I noticed our altitude was being affected as well. The Captain immediately reached to the throttles to give more thrust; but we found that they were already full forward. Shortly after seeing this and the ever increasing turbulence along with our still decreasing airspeed; the Captain turned off the Autopilot and told me as such. I was monitoring our speed and said we were getting close to our Minimum Maneuver Speed (Amber Band) when suddenly we received a climbing RA. Aware of our situation the Captain tried to be as easy as he could to get a small pitch up; but that triggered a shaker warning immediately so he let loose a small amount of pressure. I look at our RA indication and saw the aircraft was 800 feet below us. I saw we had lost about 100-150 feet of altitude. I notified ATC of our RA; but with both a climbing RA and being right at shaker with no more available thrust; we tried to maintain altitude as best we could without putting the aircraft into a higher angle of attack. We received at least one more short shaker due to turbulence and the climbing RA went to a level off. At this time we had gotten past the wave and were regaining performance. These events lasted only a couple of minutes. After exiting the gap; ATC advised us that Aircraft Y that was involved with the RA had only received a TA. We advised ATC that rides were deteriorating rapidly in that gap with moderate turbulence and mountain wave activity being present and suggested not to send anyone else through it. Shortly after (~30 mins) on the WSI app I saw the gap disappear with a full solid line of thunderstorms being present. We continued to ZZZ without incident.Cause: Heavy traffic; coupled with mountain wave activity through a small area; caused our RA with low speed event. Our normal recovery option of going down in altitude was not an option due to the RA.Suggestions: With hindsight; another route; probably a northern one; would have been preferable. That said there were gaps we would have had to go through that way; with most likely many aircraft going through them. Being very cognizant of how many aircraft through a small area with weather is the biggest takeaway.