Perhaps what you're seeing is due to the unusually porous nature of mahogany. It's got more air in it than most other woods that are used for instruments and some mahogany is more porous than others. You may be seeing "off-gassing" through the epoxy before it hardens. With your wood, a good tactic might be more and thinner coats.
It never flows like paint so it's never smooth. Ideally, each coat should be thin because: 1) It isn't cheap, and 2) the goal is to fill the pores and sand off the excess. Even with a squeegee, it is possible to leave too much on if the squeegee is used to push around too thick a coating. I'd try to work toward more and thinner coats. One of the advantages of SilverTip is that it can be recoated in a few hours without extensive sanding. So, put on a first coat squeegeed back to the wood. After a few hours, get the nubs off with sandpaper or, better yet, a card scraper. At this point, you'll probably see that the pores are not filled to surface level but that's OK. At least, the wood will be sealed. Apply another thin coat of epoxy. As Robbie O'Brien often says, "Rinse and repeat."
I haven't had much of a problem with orange peel or bubbles. I don't heat the workpiece up after application. An unscientific guess would be that abruptly changing the temperature could pull some air out of the wood.
A foam brush does work with some woods but may not be the best approach for your wood. There's no magic bullet for filling pores. It's all a PITA until you find products and methods that work for you and even then it isn't the best part of building. I've tried a number of materials and methods and now tend to use SilverTip on more porous woods, CA on less porous woods and various methods suited to particular situations.
Here's another version of the use of SilverTip:
http://www.acousticguitarconstructionforum.com/viewtopic.php?f=22&t=3062
I don't have any bodies in the fill stage now but here are two necks that are under way. The first is Spanish cedar, which has pores that are fewer and deeper than most mahogany. On necks, I apply the epoxy with a gloved finger with the goal of keeping it thin but the general approach is the same as with bodies. You should be able to see that the pores aren't yet filled to the level of the wood and will probably take at least a couple more coats to get it smooth. After these two coats, I'll level sand between further coats, probably with 220 to start.
This one is Honduran mahogany with two coats applied the same way as on the Spanish cedar.