I got a reciept from the CAA the day after i faxed my application. I got a letter from the faa 6 working days later asking me to book an appointment at the FSDO i picked.
Faxing the applications certainly speed things up. Having the FAA send a letter to an address in the US helped speed things up.
If you dont have a friend or an address to use in the US, try asking the organisation that you will be renting aircraft from if they would let you have the letter sent there.
Gary