The relevant regulations here are not the CDC's but the regulations from Belize and the State Department.

I don't know what Belize's regulations are but if they (for instance) say that you need to isolate for 10 days, that's what you need to do. The relevant regulations are their isolation rules for positive COVID cases rather than their entry quarantine requirements.

The State Department says that you need a negative test OR positive test result plus a doctor's letter of recovery. If a doctor agrees that you are recovered by day 6, then you would be able to depart any time after that. However, I believe you would need to show a positive test result from a lab. It's possible that you might get pushback from the airlines if the length of time from your test result to doctor's letter send too short (even though that's not what the regulations say).

A friend of mine recently dealt with travel to multiple following having recovered from COVID and didn't realize about the option for a letter. Some of her tests came back negative while others came back positive, so it may be easier to get the letter. If I were in this situation, the first way I'd try to get a letter is via a telehealth visit with either my primary care provider or a service my insurance provides. I don't know if they'd be willing to issue the letter, but I would try that first before trying to get in to see a doctor in a foreign country where I'm not familiar with the medical system.