I just thought of a more practical option, I can't believe I didn't think to mention it before. If you can't do this one, you just don't want it bad enough.
Watch this: How to wash clothes by hand in your Hotel Room
. Then start doing it. But you do bigger loads than the guy is doing for the demo, none of this two shirts nonsense. Large, full loads with whatever big container you have, or the bathtub itself if need be. Do it for the whole family, they shouldn't object if you don't suck at it.
The rinsing and wringing is a killer. Big, absorbent items like flannel sheet sets, bath towels, and sweatpants for larger people are unbelievably heavy when they're sodden, and they're awkward to handle because all of that weight is limp and floppy. You don't rinse "two or three times", rinse until all
the detergent is gone. You'll be more thorough if you wring each time you rinse.
I've been doing this out of necessity since my washing machine up and vanished (long story), and I can tell by the way my hands feel right now, I'm going to wind up with the grip of a bear with thumbs if this keeps up. This last time I tried doing the agitating by hand instead of with my feet, and it punished my forearms pretty good, too. I've been agitating 400 times as a bare minimum because it's been hot, I've been very active and exposed, and the laundry's pretty dirty with sweat. You don't need to do that, agitate it until your stuff is clean or you feel you've had enough of a workout for one load, whichever comes second.