Took me a day or two to find the time to play with this... but here's what happened to get everything working properly. I noticed that my headphone jack would seat properly and "click" into place. The Tascam unit would bottom out but not "click" into place... as though the jack was slightly longer or narrower than standard. Yet by visual inspection, they looked exactly the same. The Tascam tip on the jack may have been slightly more pointed. That started me to thinking that there might be something inside the phone that was preventing the tip from locking in and I thought (for about 15 seconds) about taking the phone apart.... instead (option B), I happened to have a can of pressurized air (the kind you might use to blow the dust out of your keyboard). I shot the air down the headphone jack and (tada!) that's all it took. Apparently there must have been something at the bottom of the phone's jack that moved just enough after a blast of air. In any case, the Tascam jack seats properly and if you'd like to conduct interviews with a handheld microphone (recording) the Tascam is a great (and inexpensive) tool. I'm using a Shure SM 58s feeding into the Tascam iXZ into my iPhone 4S and the fidelity is much improved over the iPhone mike (and I must admit the iPhone mike is far better than most).
Anyway, the situation is resolved and thanks for the suggestions!
kdlp