I don't know where you got your info, but the OEM Honda service manual (part number 61HA802 for 85-87 TRX250 Fourtrax) specifies the stock bore and stroke as 74 x 57.3 for a displacement of 246438.152cc
Yes, there were lost of companies making Big Bore Kits, back-in-the-day (Powroll, Cycle Pro, Shindy and others). If you want a big bore kit, there's a 2mm over Shindy kit on Ebay 85 87 Honda ATC250SX ATC250ES TRX250 Piston Shindy Big Bore Kit 260cc MX Ahrma | eBay, but, if you go big bore, you have to have a special head gasket that may not be available. I would advise just boring to .5mm (.020in) which will make it a 249779.648cc - 2mm over will make it a 259939.146cc
Honda did not have a bigger bore that was a direct fit.
Also, most cylinders of that era with a stock bore are worn to the point that a .25mm (.010in) oversize bore is not sufficient to clean the bore accurately. Consider getting a stock .50 (or larger) piston - look for piston part numbers 13103-HA0-305, 13104-HA0-305 or 13105-HA0-305 and the rings to match (you can find them on Ebay)
Have a good day
Yes, there were lost of companies making Big Bore Kits, back-in-the-day (Powroll, Cycle Pro, Shindy and others). If you want a big bore kit, there's a 2mm over Shindy kit on Ebay 85 87 Honda ATC250SX ATC250ES TRX250 Piston Shindy Big Bore Kit 260cc MX Ahrma | eBay, but, if you go big bore, you have to have a special head gasket that may not be available. I would advise just boring to .5mm (.020in) which will make it a 249779.648cc - 2mm over will make it a 259939.146cc
Honda did not have a bigger bore that was a direct fit.
Also, most cylinders of that era with a stock bore are worn to the point that a .25mm (.010in) oversize bore is not sufficient to clean the bore accurately. Consider getting a stock .50 (or larger) piston - look for piston part numbers 13103-HA0-305, 13104-HA0-305 or 13105-HA0-305 and the rings to match (you can find them on Ebay)
Have a good day