"would seem that the Advantium does both well"

Actually I've read the opposite on this forum. It seems like the Advantium can replace the toaster oven for many things, but does a terrible job of making toast. Maybe you could do an Advantium and then just a small countertop toaster (not toaster oven).

"Is it cool to just mount it in a cabinet?"

Not the OTR version.

"Finally, is there any good countertop until that combines microwave and toaster technology?"

Not that I know of. There are microwaves with "grill" elements but those are very lame.

"it would mean THREE built-in ovens"

When you say you have a double oven, do you mean you have one already installed, or just one in the plans? If the latter, I would seriously think about whether you need double ovens and an Advantium. Many Advantium owners report that they use it more than their main oven and it takes the place of the oven for many tasks.

If you do get an Advantium, make sure to get the 240V version. The 120V is nowhere near as good.

You mention mounting the Advantium in a cabinet... why not just mount a regular microwave in the cabinet and keep your toaster oven that you like?

I have an Advantium 240V from about five years ago. I read somewhere that they had a new broil setting, which I know nothing about. I may have misunderstood that. On my model, they call it broiling, but it's not like a actual broiler. There's also a toast setting. I've experimented with it. It doesn't make good toast. OTOH, I used the Texas Toast program once and it made pretty good cheese toast (thick bread with commercially sliced cheese).

I use mine regularly for the little things that people often put in their toaster ovens. It's good for heating frozen appetizers, for instance. Things it's not worth getting involved with the main oven for, but which need turning or something and so are more of a bother in my combi-steam oven. A lot of the convenience, for me, is location. It does a fine job on tidbits, though. And probably does well on other things people make in a toaster oven, like a couple pieces of chicken or a few cookies. (It can make a whole batch of cookies, but I've never used it for that.)

I keep a cheap toaster oven in a drawer just for toast. Thick home sliced breads and things that jam in a slot toaster. I have an old one of those in the drawer too. :)

In having a similar discussion with another poster a few months back. It seemed to me that they should make a combined unit and I started some searches. Indeed, there are quite a few models that are microwaves with built in toaster slots. I finally did find two that had horizontal toasting. Both are Korean. One has a little drawer on top for a slice or personal sized pizza. The other has an actual drawer underneath, like what I was proposing. One customer reviewer tried making toast in it and said it worked. I can't speak to the quality of the toast, however, or if something taller than a piece of bread or pizza will fit. That one is by LG and it seems to be available from Lowe's and Home Depot.

An Advantium does much more than a microwave and toaster oven. There are some MW/convection oven models that might work for you for the heat things up if you don't want/need a big built in speed oven. OTOH, you might love the speed functions. Do read up on what they can do. Advantiums are all built-ins, but they don't have to be over the range. There are plenty of models that aren't meant to be vents. Before you go plunking down the big bucks, however, make really sure that you want one. Especially if you mostly want it for a microwave, remember that the microwave guts wear down as much as in any other microwave, and it'll wear out a lot faster than a regular oven. It's a darned good microwave, however.

I did and love our 240 but never tried toast.
It nukes, bakes, browns(not true broil but will bubble cheese and brown it nicely). You can convection bake a casserole or a baked potato that looks like it came out of the oven in no time flat!

I also have a delonghi (similar to the breville) countertop convection oven which I store and use in my pantry.