http://bviports.org/cruise-schedule/

Jan 2017
http://bviports.org/wp-content/uploads/2015/10/January-2017-1.pdf

Feel sorry for folks visiting in Jan... That is one busy schedule! On the plus side, the 12,000 plus passenger capacity ship operated by P&O cruises is a typo I am guessing..so that's 10,000 less tourists you would have to deal with on that day! #silverlining

I have been looking for a cruise schedule for June and July when we are chartering. No luck as of yet..But! Using my great detective skills it looks like only Norwegian and Disney cruise lines operate in the Caribbean in the summer months and looking at their available cruises that visit US/BVIs, The only dates of overlap for my trip are:
June 21 (Wed) - Norwegian - We are arriving
June 25 (Sun) - Disney - We hope to be in Anegada!

FYI...Disney has a wonky schedule with 7-11 day southern and eastern Caribbean cruises but Norwegian has cruises arriving in St. Thomas and Tortola every two weeks on Tue and Wed respectively

So looks like we will be okay on that front. Are there any other major cruise lines that visit the BVIs? Looking at the schedule history looks like that is all...

We are there the same dates - June 17 to 27th. I saw on Cruise TT that we've got ships at Road Town on both the 21st and 22nd. My group will be avoiding them, too! We will be on Virgin Gorda, but we'll hang out at Bitter End and Leverick until they go away.

Aren't those 2016 dates?

I believe aarpskier is correct. There is nothing posted for June and July on that site (good reference though, thanks for the link!). Those dates look like they were for 2016.

You may want to rethink your itinerary as I am pretty sure cruise ships are in on the 21st and 25th.