When you say "baked", do you mean "boiled out?" That would be the usual treatment for de-greasing. Following up with shot blast (glass bead) would be the next normal step - at least for those parts to eventually be covered by paint.
There is some risk in both. Boiled out involves use of a hot caustic bath - and the Ford main bearings are "tinned" in place. Any flaw in this tinning give place for caustic to remain and potentially loosen the remainder of the babbitt. Still, many do this and seem to get past it.
There is some risk in abrasive blast in that the babbitt, if left, can become "embedded" with either the grit, or the products of removal (iron grit and sand dust from the casting process, essentially.) As with the caustic bath, many do this and are able to protect the babbitts by overcoating with setting rubber, caps/shields, or even duct tape works.
If one is careful and give the shops doing the work full appraisal of your concern, they will probably answer to your concern.
If you elect to remove the babbitt, then you're starting with basically a bare block much as Ford did and precautions are lessened. If you have a block which is "clapped out" and beyond shim removal/filing the caps and the crank is egg-shaped in all journals, then by all means remove the babbitt since you're basically into a full rebuild.
There are merits and downsides to both methodologies. I myself did a de-grease "spot clean" using TM4 paint stripper (strips grease and dirt too) and then hauling the block into my powerplant where I had use of the blast cabinet. I masked the babbitt, camshaft holes, and cylinders and other need to be protected areas with three layers of duct tape.
As to removing the babbitt by melting, this can be done. I've always had my concern with melting/remelting babbitt, not the least of which is a change in chemical ratio in what you catch, what plates out in the cup you catch it in, or what oxidizes and has to be removed as dross later. Most babbitt pourers don't seem to have a problem with this but I always felt it better that the rebabbitter deal with the block/rods as they find them.
I currently have a block which has come to me just yesterday. It is bored over 0.030, but seems like a recent bore. Almost NO ring ridge at the top. The rods and pistons are gone as in not present, but the crank-pins seem near to original. It may have been a period rebuild which used an original crank - which were still available from various sources up into the 1960s.
It is a little rusty, but a glaze breaker seems to clean out the cylinder bores. I've priced connecting rods and pistons and this seems like it might be a viable engine WITHOUT a full rebuild.
I'm thinking I'm going to electrolytically clean this block. I've examined online and many who do this claim electrolysis does not seem to harm or loosen babbitt - well - some who do this.
Joe K