Upgraded Dialpad Visibility Issue

My wife and I both have the 4S IPhones, and we are totally blind. Our issues involve entering menu selections or numeric passwords once the remote host answers. Often, the messge on the phone is as loud as or louder than the voice-over's voice. Quite often, the numeric pad on the IPhone's touch-screen becomes hidden. On a few occasions when the host's menu keeps yammering repeatedly round and round, I had to power the IPhone off to get loose from the phone connection. Since the numbers on the touch-screen are spread far apart compared to the old-fashioned 12-key Bell Phone keypad, we often get an error from the host because we do not get the required digits entered quickly enough. I have two external keyboards for each of us: One, a full-sized QWERTY Apple-branded keyboard; the other, a 66-key "Mini-keyboard" obtained from ATGuys.com. We can use either of these keyboards to enter and dial the telephone number; but once the host answers, the IPhone will not accept numeric data input from either of these keyboards. The only way I can input numeric data is through the damnably clunky method of arrowing through the digits and doing the SELECT key when the desired digit is spoken - if I can hear it above the host's voice. Imagine trying to enter in a timely fashion a code such as 928150 by this clunky method. My question: Is there a an APP or any way to RELIABLY enter numeric data - preferably from an external keyboard - and do it quickly enough to satisfy the timing requirements imposed on the caller by many host systems? My wife often navigates bulletin boards where she has to make menu choices on the fly; she became so frustrated with the IPhone's apparent limitation in this regard that she asked me to get her a plain "flip-phone." She uses her IPhone only for texting or weather inquiry. I "sort of" worked around my similar issue by putting the needed codes into the contact string which calls the host; but that gets me to only one item in the system. When I need another item, I often get the message, "Please enter your selection more quickly." I estimate that I get ONLY ABOUT A 10% RELIABILITY when trying to navigate the board after I have heard the item tied to my contact string. Of course, I could compose half a dozen contact strings for the same phone number but with different codes at the end; but that would be extremely clunky, making each selection to be a new phone call. A few months ago, I asked an Apple Senior Customer Assistance person how a blind person could RELIABLY enter numbers to a remote host in a timely manner, and he did not know. Of course, he could see the screen. Any insight on this issue would be deeply appreciated, since I hate to be paying for both an IPhone number and a "flip-phone" number for my wife.