Re:
This is a puzzle.
Have checked on various bikes. I have 2 Perthus 753s, both 126 OLD (one is a spare frame, hanging in the loft, still with it’s sticker from the factory).
The Shimano 600 bottom bracket that came off one of them is 115 mm. Looking at a Dura Ace 7400 chainset and BB, all 1991 (on a Gazelle 731os Exception, with stainless steel stays), the crank does pass close to the stay, 7 mm at the closest point at the pedal end.
The 753 I use a lot has a Stronglight chainset currently so no useful comparisons there, with a 17 mm clearance between crank and stay on the drive side and 19 mm on the other.
My guess is the solution lies with the BB or bent crank. As already suggested, there may be a variation in taper between the crank and the axle, allowing the crank to sit further into the frame, or maybe the axle has a left and right and somehow in the wrong way. Using a 118 mm BB might offer a solution. Alternatively, the bent crank is the other explanation, although not sure what you’d need to have done to bend it – cracked, yes, but bent, not seen.
I haven’t used a smallest cog for some time, encouraging to know there are those who still can. By the way, I use modern wheels on my Perthus, 10 speed, 130, and not a problem, even with hard use on the harsh road surfaces of the Howardian Hills, Wolds, North Yorkshire Moors and the Dales surrounding York where I live, so don't think the problem is to do with numbers of cogs.
Good luck.
