If you haven't cleared out, you might have some trouble clearing into the USVI in St. Croix, so I wouldn't try it.

I have "overstayed" after clearing out of the BVI before and always prepared had a good reason to present to any customs officers coming on board (parts of an old impeller with tools close to the engine to show I had to replace the impeller, or having a defective anchor windlass preventing me from weighing anchor {luckily, that is just a tripped breaker away from fixing :)} That will work if you are only one night or afternoon from the 24-hour limit. I have tried to to clear out of the BVI in the afternoon and when asked about my departure plans I told them "tomorrow at noon" to give myself some leeway and they then told me to come back the next day in the morning to clear out! So now I will usually tell them "tomorrow at sunrise" to prevent my having to return to the immigration offices.