Can you upload a picture of the transformer core that you have?
I used to salvage transformers from old television sets and try to rewind them... but that was fifty-something years ago. The hardest part was separating the "E" and "I" laminations because they were shellacked together, each "E" lamination alternating with an "I" lamination. Then, once they were separated I had to clean the shellack off of each lamination, polish it up with steel wool or sandpaper, make sure each piece was flat, and then re-assemble them onto a new bobbin already wound with magnet wire. You can make your own bobbin by winding and gluing kraft paper around a mandrel and gluing rectangular plastic end pieces to it.
My hand-wound transformers never performed as well as manufactured transformers, but at my young age I couldn't afford a manufactured transformer (I was still messin' 'round with vacuum tubes back then). Then along came transistors and cheap silicon rectifiers, which changed the game completely. No need for a +300 V DC B-supply for the plates, or a -100 V DC C-supply for the grids. Radio Shack started selling filament transformers, 6.3 V AC @ 1 A (or thereabouts) at a price I could afford, so I built low-voltage DC power supplies and started messin' 'round with transistors.
I hardly ever looked back at vacuum tubes after that, except when I built my amateur radio Novice transmitter, basing the output "final" on an RCA 6146B, and when I assembled a Heathkit SB-301 receiver which used vacuum tubes. I built the power supply for the transmitter using salvaged TV transformers and 5R4-GY vacuum tube rectifiers. No re-winding required. It had a voltage-regulated output using a power pentode vacuum tube and, IIRC, 6SN7GT-B dual triodes for the error feedback amplifier. It was a thing of beauty with illuminated push-button ON, STANDBY, and OFF switches, a professional aluminum chassis, and rubber feet. It weighed about fifty pounds, while my transmitter weighed about five pounds or so.
Today I operate and maintain a linear particle accelerator that uses two high-power tetrode vacuum tubes in a push-pull power oscillator configuration. Just about everyone else who owns this particular model accelerator has long ago replaced the vacuum tube version with a solid state oscillator. But if it ain't broke, I don't believe I should try to "fix" it.
Good luck learning more about transformers! A dent on the laminations won't hurt anything, and you can straighten it out after you have disassembled them. If you are real lucky there will be bolt-holes through the laminations that you can use to tighten the lamination stack and mount the transformer.
BTW, learning is what we are all here for.