If you have a Google Analytics property that you want to transfer to a different account, you need to be an admin (technically have Edit Property permissions) on both accounts, and there’s no way around this.
So, how can you move an account if you don’t want to grant admin access to your client, and they don’t want to grant you admin access?
The solution is super obvious when you think about it, and it was this morning, but for some reason last night it didn’t even cross my mind.
Create a third account! Duh.
Just make a brand new account with both you and the client listed as admins, then you move the property into that account, and the client can move the property out of that account. Once done, delete the temporary account.
Side note: whenever you create an account, you are required to also create a property, even if you aren’t going to use it. Just call it Delete Me or similar and remember to delete it when this is all done.