SDS, I was looking for sailing charters for some guests and stumbled across a few fishing chater outfits, but I cannot attest to them. If this helps, this one, Bad Dog Charters, is apparently well-regarded: https://baddogcharters.com/. I've also heard of this one, but like Bad Dog, don't know anything about them or of anyone that has used them: https://www.saltshakerbvi.com.

A little poking around disclosed that both of them are on a TripAdvisor page dedicated to BVI charters; some are fishing and others not - just cruising, but you can sort through them fairly readily. Anyhow, that page would be a good resource to check out reviews of not just Bad Dog and Salt Shaker, but also the other companies listed there: https://www.tripadvisor.com/Attractions-g147353-Activities-c61-t217-British_Virgin_Islands.html