I think it's probably best that I forget about the two-way system for now. While I want to research and do the work involved in making a hi-fi two-way system, it's not practical for me right now. I have decent full-range drivers that would give me satisfactory performance by themselves.
I found another full-range small speaker design that might be adaptable for you.
Zaph|Audio HiVi B3S single-driver
It's a long read, but it might be useful for you to see his thinking as he designed it. He illustrates with lots of measurements and computer predicted responses. It will also establish what you do and don't understand about speaker design – as a starting point.
I'm effectively replacing what a set of small harmon/kardon computer speakers have been providing for me. I bring them around with me to provide portable music. (They're simply powered single-driver desktop speakers.) I believe it will not be difficult to improve upon them.
Since I will have already made the enclosure, perhaps at a later time I can do the proper research & calculations and upgrade to a properly crossover'd two-way system.
The woofer and tweeter I named I do not currently own. They're positively-reviewed sale items on PE. I added them to my order for the amp because they cost less than my shipping. Plus, they will be good learning tools, even if not immediately applicable to the project.
Your basic idea of using a T-amp and a single full-range driver is a good one. It should be doable. The two designs I've mentioned both may be a bit large and heavy if portable is your main goal. But there are ways to make them lighter.
Designing a cabinet for bass response is more straight forward than getting a crossover right for a 2-way speaker. It's a matter of knowing three measured parameters (Thiele/Small parameters) for the driver. They are the resonance frequency (Fs), volume of compliance (Vas), and total system Q (Qts). With those 3 values, you can plug them into a number of web sites that have calculators that calculate the volume and bass tuning of a box appropriate for your driver. Such as
http://www.mh-audio.nl/spk_calc.asp#mnu_drivers.
I know of a book which explains all this, Speaker Building 201 by Ray Alden. I have a copy. There are many web sites that talk about this, but right now I can't think of one that really explains it well. Try google and wikipedia for starters.
A a side note, I noticed you're from Gaithersburg, MD. That is also where I am from, up on the North side near Goshen.
We are very close by. Keep in touch by PM if you are interested in DIY. It's my favorite topic.
I got into this a number of years ago as a way to interest my son who was then in high school. There was a science project involving something we named "the plywood doghouse", a comparison of sealed vs. ported speakers. I had fun helping. After I met a few very good DIYers in the local area, I realized I could learn lots from them. I also decided I was better at building established and proven recipes rather than buying all the gear, teaching myself how to use it all, and designing my own. A good crossover can make even inexpensive drivers sound good together. But it is also very easy to design a crossover that "sucks the life out" of speakers. It is not a simple topic.
this brings me a thought: it seems, at least theoretically, that two identical tweeters wired in series would yield a similar effect as having a resistor and a tweeter wired in series. Granted, a resistor provides a more consistent resistance, but it seems this would be practical.
A good question, hmm, let me think (as I stall for time)…
A simple resistor is cheaper…
Two speaker drivers in series is usually avoided, but never say never. There must be examples of it, but I can't think of one off the top of my head.
The voice coil of a driver has both impedance (the AC version of resistance) and inductance because it is a coiled wire, which acts as a low-pass filter with an AC signal. So the 2nd tweeter might see a different signal than the 1st in the series, and that signal might vary depending on how the 1st voice coil modifies it. It isn't impossible, but it does introduce another variable. Unless it provides a clear benefit, why bother?