There are Garden Verandah rooms with tubs, just ask for them. Also, any of the other "verandah" rooms have tubs. So, if you want to book the Garden Verandah again, just request the newer rooms. You must have gotten one of the original Garden Verandah Suites (the used to be Garden Suites with no TV or minibar). Sounds like a great trip you are planning.
The 'new' Verandah rooms all have tubs. Happy to share the map so you can see which buildings those are - email@example.com
There really isn't a bad time to go to Jamaica. We have been in January, March, April, May, August and December.
Hurricane season is the cheapest. There are about 4 price breaks during the year which you can see on their rate sheet. Humidity is worse in the summer (July, August). Temps are steady all year long. Rains varies with October, September and May being highest on average.