I have a new detached garage. The electrician replaced the 200 amp SEP in my house. The panel he installed is also 200 amp but has fewer breaker spaces. They are all occupied. Is it possible or permissible to feed a sub panel off the SEP busses without using a breaker?

I am installing a grid-tied solar system and this is the crap Challenger (named for the space shuttle) load center that came with my house. It's 125 amps single phase, so with the 120% rule I might make it work. Trouble is, it's loaded with tandem breakers that are even handle-tied. So the "General Lighting" "circuit" is 60 amps, and probably covers a god-awful assortment of 120 and 240 appliances. Also, it's half width (7") in its form factor, and you cannot get larger taller versions of half-width load centers, if you can even get them at all. I haven't worked with massive tied network circuit maps, but I assume it would impossible to untangle all of this. I'm assuming there isn't a safeway to un-handle-tie any of the circuits. And no, there's no wiring diagram for the house. Should I bite the bullet and replace it with a new box? The only change I want to make is to add a dedicated circuit for my stereo (20 amps) which would always run off the battery/inverter. As ever, thanks for your kind assistance!