Can only offer comment on Softwind (Private Homes) in Reef Bay area. We love staying there and are returning in two weeks (yahoo!) but it does not meet some of your criteria.
It is not close to Cruz Bay (relative to many others) and sits atop Cocolobo Point so isolation is its main attraction for us. There is no AC in the villa but breezes are constant except late night/early morning and mid afternoon.
Kitchen has all the necessities but not Professional if that's what you're after.
Can't tell you about cable or WiFi as we want to avoid all that when we are on vacation anyway. Check with Mary-Eileen with Private Homes. They are great people and live on STJ.
The drive from CB takes about 15 mins on average finishing on a single width road wrapping around the Point as it works its way to the top. Rules of the road are last to midpoint backs up for oncoming.
Views are wonderful South to STX, East along South Shore and West to STT.

We usually charter a six pack (Wayward Sailor last time, Breath this time)

Actually sounds like it might fit the bill. We really don't want to be close to CB. I quit drinking so other than maybe a dinner or two that's all I can see going there for. They do have internet & it's for someone in my party. I rarely make more than 3 calls home during my week. I don't mind no AC but others in my group may need some convincing. I've never been there in late April. I'm assuming the temp. is comfortable at night. Is it?
How was the cell phone reception? I have AT&T.
Is the pool decent sized, not a plunge type pool?

Thanks for taking the time. I always respond to people looking for a place that close to what their looking for. i know from experience that you rarely find the "perfect' place. But rarely have I been disappointed.

Tim

Can't help with April weather patterns and we only got reception (T-Mobile) after getting ear Cruz Bay. There is a hillside between Cocolobo & Cruz Bay. The villa does have ceiling fans and portable fans in the closets but we never used the portables.
The pool is not a lap pool. It is hexagon shaped with stairs at one end I believe deepest end is 5-6 ft but you can contact Mary-Eileen with Private Homes to confirm.
If you PM me your e-mail I can forward the floor plan and some photos. If you want to know something specific, let me know as we will be there in 2 weeks.

We recenrly stayed at Second Wind in Reef bay and LOVED it.

The house has wifi and cable, although we did not use either. We had spotty service with AT&T, but managed to get the calls we needed to.

The 3 bedrooms are all equal and very private with AC.

The kitchen was on the smaller side, but the quality of the pots, pans, etc were very good. I was very impressed with that. There is no dishwasher, but that did not bother us at all.

The decks are great, plenty of sunny spots and covered areas.

I would not hesitate to recommend it and we will stay there again. The pictures on Caribbean Villas, do not do it justice. It was so much nicer than what it looks like online.

We have also stayed at Second Wind and enjoyed it as well. The views are not as open and expansive as Soft Winds as you are on the hillside facing South and breezes are not as prevalent so the AC is nice in the bedrooms. Pool is a little smaller but not much and I think it has a hot tub. The bedroom layout is more private in Second Wind as they are somewhat detached and it has two 'outdoor' showers which is a nice touch. Both are located in the less developed Reef Bay area. Access to Reef Bay beach is a short walk down the road and through the wood. Reef Bay is not as nice as the North Shore or Salt Pond area beaches for water access.