Mudguards

Maybe, but my bet is that you're still going to struggle with clearance at the chainstays. Idk about honjos or other alu ones, but GB aren't thinner than sks. I guess cutting the existing guards after the seat stay bridge would be an option. Or maybe even cutting the equivalent sections out of the sks guards to test it first? Or maybe cutting the seat stay bridge out?

TBH it sounds easier to get a new frame:

1. Spend £60-100 on 38mm tyres
   
2. Spend £60-80 on metal mudguards and hope that crimping or whatever works
   
3. Spend £60-80 again on replacement metal mudguards because you didn't crimp properly and introduced stress risers into the last set.
   
   

... for 3mm gain?