Information theoretical security of an inefficient Shamir based access structure
Yes, your scheme is trivially correct and secure.  This follows from the fact that:


Shamir's secret sharing is correct: any group of participants with at least the threshold number of shares can reliably reconstruct the secret; and
Shamir's secret sharing is perfectly secure: no group of participants with less than the threshold number of shares can learn any information about the secret.


Since your subschemes are constructed independently except for having the same secret, the only way in which knowledge learned from one subscheme could help in breaking another subscheme is if this knowledge somehow involved the secret.  But since Shamir's secret sharing, by construction, reveals no information about the secret without access to the threshold number of shares, this is not possible.

Another way to show this is to assume that a group already has, for each subscheme, access to just one less share than the threshold number for that subscheme.  (We can do this without loss of generality, since giving an attacker access to more shares never hurts their chances of recovering the secret.)  Then show that, for any possible secret value, there exists a unique assignment of the missing shares for each subscheme that will reconstruct that secret.  (This is basically the standard proof for the security of basic Shamir's secret sharing, just with multiple sets of shares and polynomials.)

Also note that, since your subschemes are always $(n,n)$ schemes (i.e. they always require all shares to reconstruct the secret), you don't actually need the full power of Shamir's scheme.  In particular, trivial secret sharing, e.g. based on XOR or modular addition, would work just as well.