Rear wheel replacement: freewheel -> freehub and cog size changes
Yeah you're entering a world of hurt by changing one thing, and the slippery slope of knock-on upgrades start...


6/7/8 speed cassettes all use about the same spacing between gears, so they get wider as you add cogs.
8/9/10 speed cassettes all use the same width of cassette, so the cogs get closer together as you add more cogs but all fit on the same width of freehub.




Bending the dropout more sounds like a bad idea.  It should be parallel to the other dropout, and have the correct OLD spacing for your hub.

I've had to file off the backside of the derailleur hanger on a couple different bikes, but that bolt is anti-rotation and isn't doing much to hold the derailleur on.  So it can be thinned down successfully.  Its not hardened steel so a normal file should do the job fine.

Your other option is to adjust any spacers you have on your wheel to re-center it, and possibly adjust every spoke nipple to move the rim over a bit and keep it centered.

7 speed casssettes are totally available from a decent LBS, or you can order them from wiggle or CRC online.  There's not a huge amount of choice, but 12-28 is not uncommon.