Maybe a Velocity Synergy asymmetrical rim? Not cheap, but it should solve the dish problem. Do they come in 27"?
And yeah, the cushiest tires you can fit...
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1987 Nishiki Prestige (now 650B!)
1981 Trek 710
198? Nishiki Olympic 12 mixte (now 650B!)
2020 Surly Troll fat-tire build