1) Title company - tell them of their mistakes and ask for their help
2) Your agent - ask him/her to track some of the info down. Have them call the HMS rep for the area and explain the double payment, etc.
3) Start dailing the phone and call the places where you made the double payments. You should have examined the HUD statement a little closer before signing it (however, in your defense, often the title company throws it at you the day of closing and you don't have time to cross examine the nickel and dime items).
Remember, you'll catch more bees with honey and try to catch these people at the first to mid month (the end of the month is most hectic to ask for corrections to be made)
I would first contact the closing agent or closing title company and discuss the remedy to your oversite with them. They may correct the error for you or refer you directly to the HOA.
You can provide your HOA with a copy of your HUD1 and copies of your cancelled checks with a letter requesting a refund of the overpayment. I would think you can recoup all or some of the HOA expenses.