Welcome to the forum, lethargicdoc. Glad to see you posting, not just watching from the sidelines.
Is this nuc still in a 5 frame nuc box? If so, it sounds like there are ready to be moved up to a 8 or 10 frame box. If there are in a 10 frame box, perhaps it's time to put a second brood box on top? If they have drawn wax out on 7 of the 10 frames, put another box on.
The general rule of hive inspections is to do them between 10 a.m. and 4 p.m. That is when most foragers will be out. There are other factors, such as the temperature, what time the sun hits the hive in the morning, etc.
Some beekeepers scrap off burr comb because it makes a hiding place for small hive beetle. Burr comb usually contains drone brood so if you want to scrape it off, it's probably ok to do so. If you do scrape it off, take the opportunity to exam any capped brood for varroa mites. They will be reddish dots, sometimes moving around, in with the capped larvae. If you see some, consider doing a mite count.
Don't worry about not being able to see eggs or spot the queen. You have to train your eyes to see both. You saw uncapped larvae and you said it yourself, "I know the queen has been in there laying in the last 4-5 days."