I think a video call would be the best way to further pass that long verification process. It's frustrating on Op's end knowing that he has gone through a lot of processes and they're still asking for more documents. A proof of billing, IDs and selfies would be enough to know that the customer is the rightful owner of the account.
I think to finish things off, Op has to do the last 3 months stamped bill to pass this and if they will still ask for more I think that would be really too much and beyond the real essence of KYC. We all know that they also want to secure their site from fraudsters yet it will also be unfair if Op has played responsibly and spent money to play on their site.
This should be okay and I think there's no other thing needed unless they request that video call to confirm the identity of OP, its really frustrating if the case is true and someone ask for more requirements eventhough he already provide all necessary needed on the whole Kyc Process. For the readers to get satisfied with the answer and they will not get only one sided answer better for casino representative to come on this thread and explain if case is true and why they ask that long Kyc process.
I don't really think that a representative will actually show up here and clear the things up because this is not a case where they refused to pay the gambler but they have asked for extra verification, though I believe that they shouldn't do this for an amount of just $6k which isn't that much, but they must have their reasons for doing that. Casinos that are reputable generally do these things and ask for extra verification only when they find something unusual.
If Stake's forum representative takes notice of the case and confirms about it first and then clear things out in this thread, that will make things clear from their side and the public would come to know that they are not doing something bad and they are just following their KYC rules and regulations.