The point is that you have a contract with your broker, NOT the MM (that contract is between the MM and the broker). Therefore, the minute you buy shares, that contract is binding, irrespective of when the settlement date is.
If, at some stage when all the mess has been sorted out, there is a problem with supply, then your broker will be responsible for sorting it out with the MM and will give you whatever may be due to you.
Until then, there is nothing you or your broker or their MM can do.
Be patient.