The reason for not removing the top is because when it rains it pours - essentially everyday and when it comes it downpours for very short periods with very quick onset. This means that you are riding along and BOOM - it stars pouring - by the time you get the the roof up (seconds...) and even the window with the broken handle - the inside of the vehicle is drenched.
Again, if you go to STJ expecting you are at a US island resort - you will be very disappointed. I know some people have a very hard time with this concept (or understanding what it even means) - but it is what it is. You can fight it - or go with it. Believe me - you will enjoy yourself much better - going slow - and being 'over-the-top' polite, and respectful.
The vehicles are already trashed as it is - no matter where you rent. All rental agencies have a policy of 'not removing the top'. Make sure you clearly have marked all the dents/smudges in the vehicle and tears in the roof - I take photos now. The first time I rented from Conrad Sutton - the roof had a tear in the back - which they tried to put me on the hook for it - I smiled broadly - laughed - said I had photos (didn't really) and commented that it must have been the last mainlanders that tore it and how could have they harmed such a fine vehicle (it was trashed...) - and they smiled back and dropped it.
The most important thing is to try and get a newest vehicle possible - some agencies get the newer cars - and then hand them down. O'Connor's cars seem to be on the upper end of the range. Once vehicles go to STJ - they never return - the jungle just grows around them...
and yes - you don't need a 4WD - just the clearance (btw, you could certainly rent a car on STT to save a few dollars and take the car ferry over... but I wouldn't recommend this). If you like adventures (like talking the so-called 'road' from Centerline down to Cinnamon - or getting up Gifft road - or going to Lamshur Bay {sp?}) - you could not do this in a car - especially when it is wet - which reminds me - make sure you check out the tires - if bad - get another vehicle.
Added; I don't recall if I told you to check out VINOW.com - there are car rental threads there all the time - like this one (which goes to my points)
http://www.vinow.com/wwwtalk/read.php?4,87104
I haven't been reading VINOW much since I did not like how they censored information of a murder that took place there last June, but it is a good source of info.