I'd say that what you want is a Speed Oven. The ones I see most on here are GE (Advantium), Electrolux, and Miele. A cruise of AJMadison shows there are also Bertazonni, Bosch, and Smeg. There may be others that are just combos but not speed ovens. I thought Kitchen Aid had one, but I'm not seeing it. And I'm not sure all the ones I listed can broil. But it's a start. If you search on speed oven here, you'll find plenty to read. :)

I have one that will be installed soon, just not quite yet.

Sounds like you want a speed oven. However not all of them can broil. I think your options are limited to Miele and Bosch. You can engage the broiler, convection, and magnetron separately or combine them for speed cooking. Whatever you do, make sure to get a 240V one. The 120V ones aren't as fast and don't produce as good results.

I found a Miele H 4084BM for 2500. Seems like a good price. I'm fine with the microwave and baking capabilities. I want to ask the community, does anyone have experience with how this thing broils. I like to broil salmon and steam. Will this get it done? I feel like I need a flame broiler?