DH and I have done both- add a hinge where one wasn't. 401A came in the cabinet, we put a Pfaff 130 in it. And if you think Singers are heavy - try to pick up this girl LOL!!
and we've taken them out when we put the 401A in a cabinet that a 15-91 came in.
One word of warning you may also need to modify the front support. With ours, I have several cabinets and hardware, so we swapped them out.
I should have looked at your pictures - the lifts come in a few styles, and one has a bend to the base, and that fits in a specific style of treadle cabinet. Others have a flatter base and they fit easily in a newer style cabinet - typically one for an electric machine.
There was one angled base that we had to take apart to get at the screws, but most of them we did not.