I would like to understand how it is possible to pass verification, confirm your rights, so that later slushpool will transfer your property to third parties without trials and notifications?
Did (whoever got your account) add 2FA ? there is a similar
complaint, read it, might give you some clues.
With that being said, and regardless of the "not so perfect" way that Slushpool handles the authentication system, I don't think how any other pool would do any better in your situation, I mean, you don't have access to the payout address, you can't change the worker's name, all you supposedly have is an email.
To be honest, if I was running a pool and had 2 people claim they own the account, one had the username and password, and another had the payout address, I would assume the latter is the rightful owner and if both parties had access to the email address and the payout address, the last point I would use to judge would be judging who owns the mining gears mining to my pool.
But then every mining pool will have its' own judgment, but in reality, owning access to the mining gears is the only thing that matters, if someone manages to hack your pool account and your wallet, all you lose is the mining profit and whatever that wallet holds, but then owning the mining gear, you can just make a new account on the same pool or just a different pool and life goes own, but not being able to change the worker name is pretty much bad.
It means, either you are not the rightful owner (maybe you helped your friend set up his farm and now you want to steal his hashrate), it could also mean, you somehow managed to infect those miners with a virus you made which the owner isn't aware of, or in the best-case scenario, you are hosting your miners at the wrong place, regardless of how you look at it, not being able to instantly change the worker details on miners which you claim to own is worse than losing your Slushpool's account.
With that said, please keep in mind that I am not saying you are trying to steal your partner's hashrate, just trying to walk in the pool's shoes and to "justify" their actions, for all we know, your "partner" could have contacted the pool and proved ownership of the current payout address and in that case, the pool has more reasons to pass the account to him, if you want to beat him on that, they have offered you the last resort which is a prove of hardware ownership, you failed to do both, it's pretty fair that they don't give you the account IMO.