Together with the aforementioned removal of random elements, I would experiment with a few core class mechanics, especially Medics.
Ubercharges: I think there is something fundamentally wrong about mechanics that allow players to accrue power over time without a proportionally increasing responsibility/risk of some sort.
In the case of Medigun design, it enables teams to hold onto e.g. Ubers as long as they want without drawbacks. I would try to introduce an overheating mechanic like this:
At 100%, Mediguns start overheating, while still accumulating more charge. The Mediguns slowly cool down to 100% while the Medic is not buffing/healing. At like 125% the Mediguns forcibly discharge (while also providing 125% charge duration).
In theory, this forces Medics to prioritize buffs/heals with the Medigun after 100% have been reached. This would make holding harder, as a team that defends while the charge is at 100+% can't continuously heal/buff every player but needs to be strategic about it. The perfect time to push would be at 120+% after all players had been buffed, waiting any longer would inevitably starve the team for buffs to varying degrees.
Overall, this could increase the speed of the game by making holding less viable.
Other Medic related things I would experiment with are:
- increasing the amount of damage Medics deal proportional to their charge-percentage
- giving Kritz an area of effect around the primary heal target, giving close by teammates mini-crits as well
- overhauling primaries to all heal teammates at a max rate across X amount of seconds (think current crossbow but not instant) while also building charge at a max rate that keeps build times the same as they are now
- making the Quick Fix a movement increasing Medigun that matches the heal targets speed to the Medic (Scouts are fast enough) and give increased reload & firing speed on "uber" while cutting the increased healing rate currently present
I have some interesting ideas for Pyro, Engi, Heavy and Spy but they aren't that refined.
Besides class design, I would experiment with an altered version of TF2's 5CP gamemode on asymmetrical maps that are played in 2 halves with team switch. The gamemode logic exists (https://www.teamfortress.tv/53629/pc-pointcapture-gamemode) but progress is frozen as I have been putting off organizing playtests because it's hard. I am seriously considering just putting up some sort of prize pool for mixes/teams who record playtests that give the best feedback so I can finally decide how to continue development.