Checking into BVI and then back into US is really not a problem if you charter out of St Thomas. I am a big fan of flying into Charlotte Amelie.
Cannot comment on chartering out of Red Hook but CYOA at Frenchtown certainly looks after their boats and are worth a look.
In terms of timing, June and even July are very uncrowded and great sailing. This time of year, Feb & March, there is a chance of strong easterly winds and northern swells from storms in New England. But by June you can be pretty sure of wind and waves running same direction.
A slightly off beat option might be to charter out of Puerto Rico and play around Culebra and Vieques with the advantage of downhill return home at the end of the week......
We've been impressed with the condition of the Island Packets that are chartered out of Red Hook by Island Yachts. I suspect that Island Yachts, which is the Island Packet dealer for the Caribbean, probably sold the charter yachts to their owners and is obligated to keep them in good condition.
In any case, the Island Packets are not race boats, but they are a cut above the Jenneaus and Beneteaus--and certainly Hunters--that other charterers tend to provide. That said, the Island Yacht boats tend to have minimal electronics (usually no chartplotter or autopilot), but I have never had to call for a problem during the 8 or so charter from Island Yachts. We've been to Anegada, St. Croix, and the Spanish Virgins, so that says something for the confidence we have in their boats.
Having been to the Spanish Virgins, we'd advise the uninitiated that it is a delightful venue, but the facilities for bareboaters--like replenishing fresh water--are not the greatest. Dewey, however, on Culebra is otherwise a bareboat cruising jewel: great anchorage, selection of restaurants, provisioning options, and even a chandlery. Also, the moorings were free when we where there several years ago. Culebrita is the most scenic place we've visited anywhere in the Virgins.