A Singer 411G will treadle. So will a 401G. They have a knock out for the treadle belt. That will do decorative stitches and reverse and should cost a lot less than most Berninas. Reverse isn't a function of the treadling, it's a function of the machine, so in theory any machine that is put on a treadle that is equipped with reverse should reverse.
The more complex the machine though, in general the more resistance when treadling.