Have you found a solution by now? We have the same problem. Our general contractor demands a pledge/assignment so that he has the security that we will not use the money elsewhere before the payment date. All the banks we asked refuse to do an account block without an assignment...
Yes, after a lot of back and forth we finally managed it through the bank where we have the loan running. But it was a lot of hassle, a lot of going back and forth, and a lot of goodwill from those involved; it helped us that the bank had done something like this (at another branch). In my opinion, for the bank it wasn’t really a big deal – open a daily allowance account, block it, confirm, done.
All other banks refused to do it (especially if you’re not a customer). A guarantee loan is also out of the question for private individuals. A notary escrow account won’t work either or you’d have to look for 20 notaries (we tried 5, all declined).
What does your house bank say? Otherwise, if the general contractor wants it and that’s “usual,” he should ask his house bank if they will do it. What does your contract say about this point? Is it regulated? In our case, unfortunately it was, and I didn’t give it much weight at the beginning.
Sorry that I can’t show a “sure way” here; it was quite a ride for us too.