We were in a similar situation on the Westerdam this month - Grand Cayman with 6 other ships.
I found that the tendering IN was no problem. There's plenty of dock/landing space, and each ship/cruise line has it's "spot" where tenders come and go. When so many ships are arriving on a single day, they tend to "stagger" themselves - e.g. - Coral Princess anchored first in the AM, and her tenders were on the move before the two Carnival ships got anchored. Westerdam was fourth, and I made sure we got a tender before Mariner of the Seas (5th anchored) was dropping its tenders.
Can't guarantee that there won't be a "mad rush" inside the ship to get on the first tenders... hard to control that. Each line has its "crowd control" plans... make sure you know the logistics ahead of time so you can plan.
We had no trouble getting BACK to the ship either, but that's because we left Georgetown relatively early because we didn't like the crowds. We were planning lunch on shore, but the restaurants were packed by noon, so we just got the tender back. There were only 10 people on the tender going back at that time. Friends of ours had to wait a bit when they returned later, but the tenders were running pretty regularly.
To summarize - It's probably a good idea to be "Off early - On early" to avoid craziness.
The town itself was a MADHOUSE the day we were there. As I've posted previously, despite the fact that I'm a born and bred "New Yawker" - Georgetown with 6 cruise ships was worse than NYC on "Black Friday" (the crazy shopping day for Americans after Thanksgiving Thursday).
Unless you're desperate for a "deal" in shopping, I'd avoid spending any time in the town. Do a shore excursion, or arrange a private trip to one of the beaches. (Or just enjoy a peaceful day on the ship, which is what we wound up doing for the most part!)
Good luck and enjoy the Constellation - We've been on her twice, and she's a FINE ship!!