If you do decide to go the epoxy route, which is what I’d try first if this was my washer, I suggest that you use some sandpaper on each of the rusted holes first to get rid of any surface rust.  Then clean off the sanded areas and let them dry thoroughly before applying the epoxy paint.  Let the first coat dry thoroughly and then apply a second coat and let it dry for at least a day before using the washer.   I think you should get good results this way and give you at least some time to continue to search for a replacement tub should the epoxy prove not to hold on and prevent any further rusting of the holes.

Several years ago I repaired rusted areas of a dishwasher rack using epoxy paint and it held up pretty good for 2-3 years before I eventually replaced it with a new DW.  I can’t recall the brand of paint I used,  but I have used Rustoleum epoxy paint in the past on rusted metal on the outside of the house and its held up excellently, preventing a return of the rust, so that would be my recommendation.

HTH,

Eddie