How to wire subpanel back to back for portable generator
The meter panel is a &quot;rule of 6&quot; panel. You're on the right track: interlocking that is probably impossible so re-arranging things is a good plan. The hard part is that there are so many valid ways of doing the job it may be difficult to choose.
Your proposed idea is a good one. Not having done any demand calculations, but knowing that there isn't a huge difference in cost between 100A, 150A, and 200A main-breaker panels, I'd suggest you choose a 200A main-breaker panel. Keep in mind that's only its limit -- it's perfectly fine that you might feed it from a breaker less than 200A at the meter panel. You'll need to check the label on the meter panel to find out what types and ampacities of breakers are approved for use there. Finding a branch circuit breaker larger than 100A may prove challenging (or costly).
An alternative is to move the A/C and oven breakers into the existing subpanel. It appears to be convertible to main-breaker type by removing the two hot lugs and installing a QOM2 main breaker in the space at the top. Labeling on the panel will confirm. The panel is nearly full so you'll need to remove some of the existing breakers and use tandem or quad breakers to pack it tighter. You could then add the interlock right into this panel. There are two interlock kits for Homeline panels. From one glance it looks like HOMCGK2C is the one you would need, but of course you'll need to verify. A drawback of this approach is that the entire house would effectively sit behind a 100A main. If this existing subpanel is rated for more current you could choose the 150 or 200A main breaker for it, upgrade the feeder wiring to the meter panel, and put a larger breaker in the meter panel just as in the solution you originally proposed.
Another possibility is to replace the meter panel. Get a new meter-main which does have a main disconnect breaker, supports an interlock, and has plenty of spaces available. It is perhaps daunting, but the process goes something like this:

get building permit if required in your area
ask electric utility for a temporary disconnect (my utility does this at no charge)
remove the old panel, install the new
get work inspected
ask electric utility to re-connect