I've never used a grill like yours and therefore I don't know how hot it gets, but some portable gas grills work fine. It's true that very small, cheap (around $50) ones don't usually produce enough heat.
With regard to the butter, I suggest you either use a food processor or soften the butter in the microwave before you add the herbs and other ingredients. Either way, you can use the mixture immediately after mixing -- no chilling required.
If you don't have a food processor, try heating the butter in the microwave for 1 minute at 10 percent power. If isn't not sufficiently softened, heat it for an additional 20 seconds at 10 percent power. Once your butter is softened, transfer it to a bowl and stir in the other ingredients.
I like to freeze compound butter in cubes for later use, but you can also shape it into a log, wrap it in plastic wrap or parchment, freeze it, and cut off as much as you need.
Personally, I never sear steak in a non-stick pan because a traditional pan develops more fond (browned bits) than a non-stick pan does. If you do decide to deglaze the pan in order to make a pan sauce, fond means more flavor.
I'd never cook meat on a large quantity of salt (if I interpret "bed" of salt correctly). You want the meat to come into direct contact with the pan.
If you finish the filets in the oven, don't cover them, or they'll steam and the sear you put on them will soften. Taking the meat's temperature is a better idea than cooking for a set number of minutes. If you want the best flavor, don't cook filet mignon past medium-rare. You do want to cover them lightly with foil while they're resting, however.