Monopoly millionaire mortgaging of a property to pay for another property
I would say no, you are just out of luck. 

Defining Bankruptcy

Since the rules I found here don't explicitly define bankruptcy, but merely list the changes from standard Monopoly rules, I will refer to the standard rules. It states 


  BANKRUPTCY ... You are declared bankrupt if you owe more than you can
  pay either to another player or to the Bank.


Since the rules for Millionaire state about mortgage (and other things)


  IMPORTANT: You can ONLY do these things if you’re bankrupt, not under
  any other circumstances!


Since buying property is optional (the standard rules say that you may buy property when you land on it, it is not required), you don't qualify as being bankrupt.  Since you are not bankrupt, mortgaging is not an option.