Quick reply before I go to bed: So your modem is a Pantech UM175 for the EVDO network of Verizon (and not the newer Pantech UML 290 for their LTE network as I had previously speculated). I've only had time for a very cursory search, and I'm therefore not yet 100% sure whether it needs the 'usb-modeswitch.tcz' extension or not (with a current hunch that it won't require it). In any case I'm rather optimistic that it should be possible to get away with only a very small number of required extensions.
My count of ca. 30 extensions for NetworkManager was anyway far too low, as NetworkManager needs to operate within a DE like LXDE or Gnome for it's GUI to be usable. Which means that far more extensions would be needed. But in any case I'd see myself unfit to provide assistance with such a "monstrosity".
Finally I see the need to point out that a 12 MBytes download like TC can not possibly support all potential networking modes "out of the box". That is one of the reasons why Puppy weights in with ca. 129 MBytes and Ubuntu with ca. 695 MBytes. In this case of "you get what you pay for" the first target of TC are ethernet connected systems (which are still IMHO the vast majority of users) and more support (e.g. for WiFi) comes with the CorePlus "edition".
I'm not sure how to reply to that. Let me just state the opinion that a serious operating system ought to be no larger and no smaller than required to backup and restore itself and to connect to whatever repository or medium contains additional functionality. I think Puppy contains more than it needs to, and TinyCore perhaps less... and Ubuntu is nothing less than a fat slow pig. I've been looking at distros for two months now, and TinyCore is the one I feel has the most potential. It's also the fastest to boot, with Puppy coming in a fairly distant second. But booting isn't enough if you can't get to the goodies, eh? <g>
(I'm also puzzled that Puppy is the *only* distro around that seems able to 'reboot' my system, an Acer D257 netbook, including TC and Ubuntu... although when I first installed Ubuntu both 'reboot' and 'hibernate' worked... still tracking that one down.)
My plan for tomorrow would be to give you some guidance how you can make use of your working Puppy configuration (which IIRC uses 'wvdial'). It would be therefore good to know which Puppy release you have been using.
If you can't wait: try to google it yourself, as there are several other people who have used your modem and 'wvdial' on the Verizon network (e.g. here). In theory you'll require the following extensions: pppd.tcz, wvdial.tcz, libssl-0.9.8.tcz, and wvstreams.tcz (plus a dependency file).
I'm not in a great hurry, I'm able to use Ubuntu to do everything I need to do, as long as I don't mind scratching my ear with my elbow. I'm not sure how we're going to bootstrap this modem into operating without the appropriate extensions, but I'm more of a bits'n'bytes developer than anyone who has spent a great deal of time installing anything. I have the latest stable Puppy, 5.2.8.
I would suggest that someone consider just how large an initial iso would really need to be in order to really do the setup job and make a decision; maybe that's already been done. Maybe if it's too big, what you need is a leaner setup program, something fullscreen character mode perhaps.
I'll check back in the morning, probably between 0700-0900 UTC, but as I said I'm in no great hurry, I've half a dozen projects on the fire but none are urgent. Thanks for your continued efforts.