Rebranding an ASIN using a brand from a separate account

We’re splitting several of our products off into a separate business with a different brand. We already have the brand registered through a separate Amazon seller account.
There’s a rebrand support category in seller help, but is it possible to rebrand using the brand in our second account? It’s for an ASIN we created.
I tried uploading a product template in our new account with the new brand, but received error 8541:
“The SKU data provided is different from what’s already in the Amazon catalog. The item_id data provided matches ASIN XXXXXXXXX, but the following data is different from what’s already in the Amazon catalog: brand (Merchant: ‘Our New Brand’ / Amazon: ‘Our Old Brand’). If this is the right ASIN for your product, update your data to match what’s in the Amazon catalog. If it’s not the right ASIN, make sure that your data for item_id is correct.”
I created a support case, but don’t have high hopes based on past experience (will likely be a cookie-cutter reply about ensuring the product template has the correct brand).
Is there a better way to approach this? For example, should I try transferring the new brand to our primary Amazon account, changing the brand for these products through the primary account, and then transferring the brand name back to the new account?