I can only speak for the week after Thanksgiving, but...
We asked the SP beach carvers the same question and they told us that no ships were expected on Mon & Wed. This info was entirely true for then as we went fishing on Mon (no other boats in sight) and did Hol Chan/SRA on Mon (had both sites ENTIRELY to our wee boatload of 4).
The carvers also mentioned that if you're more likely to do HC/SRA as a half-day rather than a full-, book an afternoon excursion as the cruisers need to be back on-board the big ships by 2p.
Love those carvers!