Sandra, I forgot to mention I did try once with 50/50 butter/shortening instead, because I had a stick in the fridge. Same outcome as far as taste (although it was really firm when chilled--as in sculpt-a-copy-of-David firm). I've also tried with SB/shortening/coconut oil; same thing--kind of a tropical-cream-cheese flavor.
I like the idea of extra vanilla (it is my favorite flavor frosting!) You also mentioned mixing a small amount of real sugar to offset the odd flavor of the stevia. What was your stevia-to-sugar ratio? I'm wondering if that would work here; perhaps 1 Tbsp sugar plus the sweetener equivalent to equal 1 1/2 cups total "sweet stuff"?
Also, I had a flash of inspiration (or insanity): I thought that unlike cake batter, with all the flour, eggs, etc., there aren't enough other ingredients in with the sweetener to act as a "heat buffer" against the direct heat on the pan--which perhaps chemically changes the perceived taste of the sweetener. Would cooking my frosting base in a double boiler help alleviate that, or am I just setting myself up for a failed roux that won't cook thoroughly/thicken properly over the indirect heat?
Yes, frosting made with butter does become very firm (maybe not quite "sculpt a copy of David", lol!) when refrigerated, but it softens once brought back to room temperature, just like plain butter. BTW, the tropical cream cheese taste sounds delightful to me!
I put extra vanilla in all recipes. If the recipe calls for a teaspoon, I use at least a tablespoon. Gets pretty costly these days! My point, it surely will not hurt anything.
When I've used Stevia, which is not often, I used approximately 1/4 cup of sugar per every 1 cup of Stevia. My husband couldn't tell the difference when I used no sugar, but I could. The small amount seemed to completely mask the Stevia taste. I've used it only to see how it would work, so not a lot of experience. Again, good idea to try 1 tablespoon of sugar with your other sweetener to see how it works. You have nothing to loose.
I don't know if heat could change the flavor, but it is a definite possibility. Using a double boiler should not affect the way the mixture thickens. I use one all the time when making custards and any delicate sauce. Since the mixture would have to reach the same temperature to properly cook and thicken, regardless of whether or not you use a double boiler, I'm not sure if it would make a difference. It certainly would not do any harm to try! The gentler heat and slower rise in temperature could do the trick.
If you try any of these things, please let us know how it turns out. Good luck!