So the answer is that, for the time being, there is not an automatic way to do this unless the two site sets have identical quantum number types (so basically, no useful cases). The reason is that although the site set class design is quite flexible, the QN system is currently less flexible (for efficiency reasons). The QN system currently requires that all QNs throughout your code are globally the same, in terms of having the same number of active "slots" with identical modulus numbers in the same ordering. If you just took two of the site sets provided with ITensor and merged them, they'd have different quantum number definitions.
I've been thinking for a while that I should upgrade the QN system to include string descriptions of the different numbers inside the QN. Doing so ought to make it possible to do what you are asking.
For the meantime though, please just define a new type of site set that returns different site indices depending on the site number, but with the same kind of QN on each site, as in the example you linked.