Idk if it’d work but if you have a bench with legs in the middle, you may be able to wrap the front and back straps around them instead of the seat to hold it from moving. Depending on the bench you may also be able to screw some hooks on up underneath the bench that can hold the straps too. Or if they do fine without a back, you could try just a cushion style.
I have a convertible highchair that turns into a booster as well as a small table and chair set