Have you linked your Vanguard clearing account to your Fidelity clearing account?
If so you should be able schedule on Vanguard to make a fix $ distribution to your Fido clearing account on whatever date best fits your distributions.
For example, if you know every month you have $100 of distribution in your Vanguard cash account by the 10th, schedule a transfer to the Fido clearing account of the desired amount a couple days later
Personally not having a lot of confidence in Vanguard' administrative excellence, I would set my transfer amount below the expected total to be sure it did not get kicked out. You can then always tune once you get confidences all the parties are doing their thing. I suspect you will need to manually intervene at least at year end to cover any mutual funds year end $