The 100A breaker is overcrowding the other slots for a reason: to enforce stab limits. Even a stopped clock is right twice a day, and FPE got that right.
If you did what you wanted to, you would have 130A on those two stabs. That's over stab limits for a lot of modern panels! If you've ever seen panels where the main breaker is in the upper left corner and nothing is allowed across from it even though there's nothing wrong with those spaces, that is why.
So if you have felt righteous to do this because you feel you are working around a panel defect, no. This is a plain case of playing swap-the-breaker on an overfull and overloaded panel, with known stab-reliability issues, doing the very thing that has everyone spooked.
The 100A breaker is not double size. It is normal size 2-pole. The other breakers are double-stuff. This is a 12-space panel with 8 spaces double-stuffed. A 12-space panel on a 200A, all-electric house. One has to woder if this was permitted in the first place!
Kill it with fire before it kills you with fire
If you're family, stop fooling around and swap the main panel. It's not any harder than a subpanel, you just have to work in the dark because the meter is pulled. Shop smart for a 40-space of a sensible physical dimension (CH, QO) and combo-pack that includes some breakers. Don't even attempt to solve AFCI or GFCI issues, aluminum wiring issues (loop back on those later, just use Al-rated breakers) etc. If the AHJ insists on increasing project scope to include ancillary stuff like that, then just don't pull a permit and do it underground - but do it correctly. Do double-check your wire sizes - I see too many 30s and not enough 15s.
If you're a contractor, run... this panel is a fire-starter, and if one does, your insurer may decide you're on your own!
Why not a subpanel?
Because I don't believe it's a significant cost savings over just swapping the main panel, it's a band-aid on a very bad situation, and the heat needs the whole 100A, there isn't spare (electrical) space in the subpanel for anything.