Why not just on a foul on the floor, inside the last 4 minutes, the team with the ball gets the choice to shoot or take it out? Like football where you can decline a penalty. The Elam Ending seems like an idea to up the entertainment value, which is fine for stuff like TBT, but seems like something that isn’t really needed for NCAA.
Regarding option discussed here for the FTs or keep possession choice for leading team, it could be made to work with the proper balance of details. I think CBB experimented with it in early-season games (maybe back in the '90s (?)) and it was dropped before the experimental period officially ended. Can't recall exactly why, but it proved unpopular.
A reason I think it's worth considering, in some form, isn't only the time required for the FTs themselves, but a lot of the fouls happen in backcourt and it eats time for everyone to go to the other end, set up their positions on the lane. If a main goal is to reduce interruption of game flow, that rule change couldn't hurt, and might not disrupt strategy too much.
Feel free to poke holes in my analysis, for purposes of discussion.
I do not know why a team would ever decline the FTs, though, unless the foul was on a really weak free throw shooter. You are likely to end up with more points out of the possession on the line than you are just trying to run some clock on them.
Running some clock risks a turnover and/or the other team can just keep on fouling you, meaning the end of the game can take even longer than it would otherwise.