I'm betting you will be able to make weight with a heavy palma barrel. I have a Barnard action, which is considered heavy by some, with a 34" heavy palma and I make weight.
If you weigh everything you have, including rings, bases, etc., you can use a barrel weight calculator to determine what will work and keep you under the limit. Lilja has one on their site that is accurate to less than an ounce. You can also take measurements on your current barrel to determine its weight if it is already on your action. This is will allow you to figure out how heavy you can go. I would figure in a 4-6 ounce leeway in for scale variations.