Dialing numbers from Contacts on iPhone when using a calling card or callback service

I've got a long distance calling plan where I call a number and get a busy signal. The service then immediately calls me back, and when I answer, I'm presented with a dial-tone at which point I can call any number I want, with really cheap rates, while only getting dinged for local incoming minutes on my iPhone.

The problem with this is that I can't find a way to access and "dial" numbers from my Contacts when I'm presented with the dial-tone. I essentially have to have the number memorized or written down beforehand.

When given the dial tone, I can access all my contacts, but there doesn't seem to be a way to generate the keypress tones from them.

Is this possible on the iPhone? Maybe some other app that I can launch after answering the call which will access numbers in Contacts and generate keypress tones?

Could you try accepting the incoming call, then starting a conference call where you dial the 3rd party? The dialing might make noises that the calling card service can hear, then you disconnect from the 3rd party before it connects and bills you.