Two things:
1) do the 1922 have to be completely separate from cabinet posts? I think you've implied that.
2) how funny would it be for Labour to "accidentally" have 122 cabinet posts just for the lols.
Yes. Traditionally the 1922 are all backbenchers - so non-ministerial (or shadow-ministerial).
You need about 95ish shadow-ministers to do it properly, but you can skip them or double up roles.
Which is what the Tories will now have to do. They don't have enough qualified MPs.