“Could you recommend an exercise with the goal of reaching max heart rate in the shortest time (for a 4 min Tabata)? For ex, would light hang snatches work? Would isometrics work? Any info would be much appreciated.”
Snatches would work, depends on how light you go. So would isometrics.
There’s lots of possible options.
Jump rope, doing double or triple unders, depending on skill level.
Single or double kettlebell complexes
Basically, anything that moves the body a bunch and/or a weight around a lot is going to do it. Isometrics in attempting to move something immovable fit this bill.
Many of these exercises, the bodyweight ones anyway, are covered in The Ultimate Guide to Bodyweight Conditioning.
The more strength you exert quickly the more it should jack up your heartrate. The other side being you have to be able to sustain the ability to do that in a safe manner.
Just recently I’ve got back to doing hill sprints. While not in a Tabata protocol (that is 20 seconds of work, 10 seconds of rest, repeated 8 times) it’s somewhat similar.
Understand that the Tabata protocol was originally designed for use with an exercise bike. It allowed you to go 100% speed quickly and safely.
This became famous and spread across the world as the creator Izumi Tabata said “The rate of increase in V02max is one of the highest ever reported.”
Any other exercise may not deliver exactly this. You’ll really have to play around with the exercises, and weights used, to get it right.