There is no way to transmit data wirelessly without being susceptible to trilateration (using the standard definition of "radio wireless").
That's why attempts to "transmit data without revealing your location" usually end up shifting to things like laser, infrared, or other visible light methods. These things tend to work well in directional applications, which is why they're either static (like MAN) or military (for whom the benefits of secrecy justify the trouble of maintaining directional links with mobile and semi-mobile equipment).
(Which is, incidentally, the point I was going for with the motorcycles. If you want non-detectable wireless transmissions, you have to use something other than a radio, and that was a spectacular example).
There's really only two ways to mitigate the the ability to ELINT radio transmissions:
- Make them directional. Requires special hardware, works better for some types of radio than others, not really worth it (if you're going there, use a laser).
- Lower the power so that the opponent has to be physically closer to triangulate. Of course, in turn, whoever you're transmitting to has to be closer than that. And you don't seem to trust the network operator, so that won't work.
Now, you stipulate that
parties are using only standard equipment (not specialized equipment
specifically designed to track users)
That's kind of a difficult stipulation. You can walk your wifi laptop into most businesses secure in the knowledge that their system isn't set up to locate you. But getting a system to do it isn't difficult. And heck, just like Pringles cans weaponized armies of hackers, you can put together your own FindMe pretty easily. I think it's fair to say that anything you can transmit with "standard equipment" can be located by an opponent using off-the-shelf or homebrew devices.