Hi WIllie_S,
Yours is a good question. Your idea is done often, but a couple of things will pose challenges to you.
The below answer Assumes U.S. and Covered by NFPA 70:
Lots of FPE load centers didn't come with doors. If yours is like that, when you remove the breakers, you'll have to make a cover plate That voids the whole Listing Agency approval thing. The inspector might knock it down. Or, find a bunch of snap-in blanks on the used market.
Also note that if you are removing a bunch of conduits or cables, you'll have to close those openings.
I like Loto_Arusu's advice to purchase a pull box to replace the old load center with. You also could use a steel gutter section vertically if there were conduits or cables coming out of the side of the existing load center. It'll make the swap easier. They come with or without knockouts and with hinged or removable covers.
You mentioned a water heater in the way. If it's blocking the FPE panel, you'll have to move the panel anyway. Might as well start new. You can get them in plastic or steel. With or without knockouts in steel.
Take a study of NFPA 70 Article 314 for sizing the new box.
Don't throw out the FOPE breakers, especially if they are Stab-Lok. They sell for stupid money on places like eBay or Bonanza. Used breaker buyers will also purchase them, but for less money. Check ElectricalAdvertiser on line.
Paul