Multi-sig N of M where 1 of the keys can see the balance but not spend (read-only key)? If I had a non-HD multi-sig wallet, checking the balance of it would be trivial (I would just look at the blockchain to see the address' balance, without the need to hold a key).

However, with HD wallets, a wallet is comprised of N addresses. So knowing the balance of this wallet is not easy unless you are one of the key holders.

Therefore, this is my question: how to know the balance of a multi-sig HD wallet, from a read-only standpoint? Can the distribution of the keys be asymmetric so that there's one key that allows checking the balance but doesn't allow signing?
The author of this paper seem to have put some thought into the problem you describe and has proposed a solution that seems relevant to your question:

A new HD wallet that tolerates key leakage
Master key generation. Instead of one master private key, our HD wallet uses
m master private keys ˆd1, . . . ,ˆdm for some reasonably-sized m to be determinedby the requirements of the wallet. (For example, in the combined treasurer-auditor use case of Section 2, m must exceed the number t of departments in the organization.) To keep the master private key size down, these master private keys could be generated pseudorandomly with no loss of security using, say, therudimentary deterministic wallet described in Section 1.*

https://eprint.iacr.org/2014/998.pdf