Again the longer one with the silver is from CF-29 MK4 and earlier.
As you mentioned, it's too long for the CF-30 without making a few modifications but I'm happy to have it for testing!
You can not apply formulas that are intended for a dipole or a ground plane to a wound manufactured antenna. As you have stated, you may be dealing with capacitance hat, or a bottom load, the tightness of the helix and even the diameter of the antenna wire all effect the "Q" (Bandwidth) and frequency.
Here a quick test, do your intended formula show the antennas to be the correct length, if so, you might be on to something. Generally speaking, the frequency is what the manufacturer says it is, for it's intended application. Does that mean we have to listen to them, well I never do...
That's a hard question to answer. What complicates the issue is that all WWAN cards support several bands, either as multi-carrier devices or network fall-backs for the sake of coverage while roaming on partner networks or switching to 2G. Some even use different bands for upload and download, like AWS. So obviously there are compromises that have to be made. Granted, they may choose the "main" band for a particular carrier and optimize the antenna for that. So here's a better question that might be easier to answer: when Panasonic ships a system for use over Verizon, Sprint, AT&T or for Europe, do they ship with different antennas? In other words, do they have carrier or band-specific antennas with different part numbers?
Yeah, calculations are all different for dipole, monopole, inverted-V, etc.... Luckily there are online calculators for that. Toughbook antennas are obviously monopole so relatively easy to figure out. And then there's the issue of half or quarter length. For example, 1200Mhz is 2.34 inches HALF length but 2100Mhz is 2.67 QUARTER length. So the same antenna can roughly
be used in both cases.