flagship,
The Stalker model is the one that comes with the synthetic stock.
It does not come in stainless. It is also about a half pound lighter than the wood versions.

If you are really set on stainless you may need to go with the bolt as others have suggested. I don' t know if you can have a stainless barrel fitted to it. Seems like you should be able to, but the action will still not be stainless.
I think the stainless craze may be a little overdone. People hunted for a long time with non stainless rifles in every kind of weather and seemed to do ok.

You can coat the barrel and action with a thin wax on the outside and it makes it pretty weather proof. If your barrel or action get wet on the inside you need to give them a quick clean even if it were stainless.
From your questions it sounds like you will be using this rifle in a wet climate.
The key to the BAR is keeping it clean and rust free so the action will cycle reliably.
If you do you should have no problems.

The BAR is a good rifle. As accurate as the average bolt action, sometimes more so.
Excellent choice for hunting thick cover where you may get a couple quick shots from a less than ideal angle, where with a bolt you would only get one.
The other benefit is the action soaks up much of the recoil eliminating the need for a muzzle break.
I definitely recommend you try one without the break before you buy one with it.
Shoot one once without ear protection and you will not want to do it again.