OK. I did a little (well, more than a little) research on this after someone eluded to it earlier in this post.
Do a search for 'DTMF VoIP talkoff". The random beeping is what is called 'talkoff'. It seems to be common with VoIP equipment. High end VoIP phones/ equipment allow adjustment of this to reduce or eliminate it. Some routers that include VoIP also have this setting. Apparently MJ does not (there's a big suprise)
In my experience with MJ after 2 weeks, my voice seems to setoff more #1's and 4's. Everyones voice is different and, my guess is that, unless they come out with an MJ that contains the circuitry required to allow DTMF talkoff squelch capabilities, then they will never completely eliminate this problem for everyone.
I made the adjustments posted by Thunderstruck (Thank you) and started exclusively using the computer headset/ softphone combination. I was on the phone ALL day today for my job. I asked each person on the other end if they heard any beeps or what the quality was like. All said they heard NO beeps and that, had I not told them I was using VoIP, they would have sworn I was using POTS and would never have known the difference. I have RoadRunner with 8Mbps and a Netgear 802.11g router and, I had the 6-19 update on the MJ.
For 40 bucks initial investment, I will keep this for a year and, if something better comes along, I'll reduce the MJ to dust with a sledgehammer; much like the guy destroyed the fax machine in the movie Office Space.
Hope this helps everyone.