I now have several bikes with Machined shim sleeves post is 27.2.. Ooodles of choices there.

Sleeves with a 27.2 ID and what ever your seat tubes ID are as Its OD work perfectly

[FWIW, 1.25" is , 31.75mm so rounding.. .6 under , .8 over....]

seat tube of frame could be distorted... a bike shop with an adjustable reamer can cure the misshapen frame tube back to round..

To make your 31.3, you can get a shim sleeve and take of 0.5mm from it and not damage the actual seat post ... (which it reads like you have already done)





Patience, grasshopper..
...