You can fix the off centre hole by checking the run out and carefully open up the hole with a needle file to centre it. Then you simply mark with a pencil on the label which part of the elongated hole butts up to the spindle for next time.
Option 2 is to drill/mill the hole oversize. Then centre the record to minimise runout. You can make it easy by making up a washer with a spindle hole, and once you are happy that you have found the true centre, then push the washer over the spindle and glue it to the record. Now you have a record with a true centre.
PS As Tony has pointed out, dont assume the record is round, it isn't. You must play the record and work out how far it's out by measuring the lateral movement of the stylus.
PS2 : As this advice is free, there is no responsibility on my part if you screw up.
Option 2 is to drill/mill the hole oversize. Then centre the record to minimise runout. You can make it easy by making up a washer with a spindle hole, and once you are happy that you have found the true centre, then push the washer over the spindle and glue it to the record. Now you have a record with a true centre.
PS As Tony has pointed out, dont assume the record is round, it isn't. You must play the record and work out how far it's out by measuring the lateral movement of the stylus.
PS2 : As this advice is free, there is no responsibility on my part if you screw up.