Well, to convert an old cast iron flat bed to a free arm you will need the following :
Hack saw, Welding equipment A full chest worth of mechanics tools etc.
get the picture ?
It isn't that your request is silly, it isn't But, sewing machines ( like most other equipment) are made one way to stay that way. Ever notice that when there is a choice the free arm version is always slightly more expensive then the flat bed ? that was nothing to do with the " extra feature" that is the free arm.
Flat bed machines are just easier to make. Various parts can be spaces out more freely, push rods can be straight, and so on, which also makes the thing easier to assemble. And so more affordable.
Free arm machines need to have their parts fitted in a much smaller, narrower space. and conscequently are "twisted" to fit, since more parts occupy a smaller volume they also are mode difficult to assemble.
Ever notice that there realy weren't that many free arm machines before electronic machines became popular ?, that is because electrnic machines usualy come with multiples motors ( one for the feed dog, one for needle going up and down, one for the needle going side to side). All these motors are controled through wires, Older mechanical/electric models were driven by one motor and all the functions were there results of cams and pushrods and power trains, all these had to be position relative to eachother. In an electronic machine each motor can be where ever regardless of the position of the others and each is independently controled by a computer and connected by wires, So they can be fitted any which way the maker chooses.
so there you go , I hope I didn't bore you but that is, in a nut shell, why you can't do what you wanted to do.
Sorry
Jean