Can I renew my Non-O Retirement Visa in Thailand earlier than its expiration date and change the expiry date?

In Bangkok you can apply for a new extension when you have 45 days or less left on your current stamp. So in your case you can apply any time after June 5th

Unfortunately you can't move the renewal date AND the extension you apply for (even if you apply 45 days early) is dated the same as your current expiration date

The only thing to do would be to leave without a re-entry permit, let it cancel and then either get new Non-O in your country before you come back or come back here on a visa exempt and start the whole process over. There is no way to "adjust" your expiration/renewal date other than that