We're now considering setting up the multisig with hardware wallets and then wiping the seeds off them and only storing the seed backups in the secure storage locations. When we need to spend we recover the wallets from the seeds at each location. Any issues with this?
Most important thing for single setup is to add passphrase as additional level of protection for your seed words and keep it in separate location, so even if someone finds your cryptosteel he can't use it without passphrase.
Topic of multisig wallets is more complex subject and not all hardware wallets are fully supporting Multisig, for example in case of Trezor and Ledger you can't construct and verify multisig and that is a big flaw.
You can however use those wallets in combination with Electrum cold storage and other hardware wallets that fully support Multisig like ColdCard, Keystone or BitBox.
Don't overcomplicate things with seed backups, some people keep them in deposit boxes, other give them to family or friends who don't know anything about Bitcoin, put them in ground, etc.
Reset of hardware wallet is a good option if you don't plan to send or receive funds for a while.
Hardware wallets aren't meant to be used as cold storages, unless you haven't an air-gapped laptop left and taken the necessary security measures.
Hardware wallets are meant to be used exactly as cold storage, because they are small computers not connected to internet, some don't even have cable connection with computers, and if they do have USB connection it is made in a more secure way.
There is no increased risk in storing a hardware wallet together with its steel backup if we assume storage of the steel backup is secure.
You should
NEVER keep your hardware wallet in same place with your seed words!