What are the ways to get FireFox (or another browser) to play YouTube videos, rather than open the app? Of those, are there any that work on a relatively low-end phone ?
You need to clear the default setting to open YouTube videos in the app.
Go to settings -> Apps -> YouTube -> Defaults -> Clear defaults
You can use any browser that supports streaming. You type in the address bar or Google search for YouTube. Tap on the link for YouTube. Then search for your video(s). There maybe some buffering issues on low-end/legacy devices. You can change the quality of the stream (ie. 240, 480, 720p). Aside from that, make sure all background processes are shut down and you don't have any other running apps.
As to which one works best, that would be an opinion and not correct forum for this. Although I just use stock Android browser.