Bar end shifters onto a flat bar - temporary fix solution
Go find a scrap donor bike - either check at the local refuse-resell shop, or a bike cooperative.   You're after one with friction lever shifters.
A simple friction shifter will move as many gears as you want, and won't cost a lot.  They're super-versatile and are well-worth holding onto for situations like this.
I used one to shift a quad-chainring bike, and it worked really well for that purpose.