Move your coins to a segwit address, and not a legacy one, if possible. This time you'll pay more fees but next time you move them, for any reason, you'll pay less.
To avoid high fees, you may find this web page helpful:
https://bitcoinfees.earn.com/Usually, on weekends the fees are much lower because there are no many transactions.
Good luck and let us know what happened, I haven't claimed my bitcoin Gold either.