I think phea's suggestion would do a lot to alleviate stalemates tho it might be a cp_steel situation where people get incredibly confused with all the entrances that open/close and in very specific circumstances. Also in that scenario are teams on last going to risk doing "another midfight" on point 2.5 where if they wipe the other team will cap their last.
I think the idea of a neutral objective forcing a fight is a cool one and possibly the simplest way to do this would be to create a neutral pickup similar to something like the quad damage. You could make it spawn with a certain amount of time left on the roundtimer and have it give a player a certain number of seconds of crits etc.
If you make pickups like these spawn in the right positions and with the right timings then you can have them dictate the gameplay and teams would be able to play around them without making things seem totally unfair. They also make sense as pickups are a thing that already exist in the mannpower mode (even though that mode is fucking terrible) so probably wouldnt be too difficult to add into the existing game.
e.g. picture the scenario that 2 teams are stalemated between mid and 2nd on badlands- a pickup that could win or lose a fight spawns at 6 minutes left on the roundtimer in badlands house in the area close to resup/haunter. Teams can rotate players to get this pickup but it puts players from both teams in a compromising position to play for this, and allows the enemy team space to make a push or contest the players playing for the pickup.