Your best bet is probably to respace your hub by moving a spacer from the left side of the axle to the right side. Or, if it's a 130mm OLD hub, you could add a 5mm spacer to the right to make it 135mm and widen the rear triangle. Presumably you've already widened the rear triangle anyway.
If you do this, you'll have to redish your rear wheel slightly.
I tried using a 7 speed , but ran into the same problem, so I ended up putting a 6 speed on. Works great. The biggest problem was getting the RD to line up right with the rear eyelet, actually had to file the Rd hanger for it to work.
Yeah spacers or grinding and adding a fillet weld is pretty much the only way. Or you could get new dropouts fitted that emerge from the inner edges of the stays. I think if you cold-set the stays outwards a bit before attempting to respace the you may find you have enough space. Six speed is probably a better idea though.
Thank you very much for your suggestions. Repeating some of your ideas I also thought about replacing the hub's axle for a 135 mm axle and adding spacers on both sides of the wheel, filling and brazing the seat stay, but in reality I will manage with 6 of the 7 sprockets but I will need a custom cassette. Something like a 19, 17, 15, 14, 13, 12, 11 cassette with a 53, 42 chain wheel set on 451 rims will suit me for the meanwhile.