Currently the only way to expand your area of control is through radars. If you try to pan the camera into unexplored chunks, the scenario won't allow it (well, with some exceptions).
I'm considering changing this, and I'd like to hear your thoughts on it.

Alternative 1:
Allow any exploration. You can pan the camera around and reveal areas freely, just as in sandbox mode. This removes some challenges, such as discovering resources/enemy bases, and makes radars less important (thus reducing electricity usage significantly).

Alternative 2:
Allow exploration when in vehicles (car, tank, locomotive, etc.). Keeps some of the challenge of discovering resources/enemy bases and keeps radars more important until you research automobilism. Can cause some issues, such as leaving a vehicle when outside of the area you're allowed to view when not in a vehicle.

Currently I'm leaning towards alternative 1. Earlier I planned to make this scenario PVP-compatible, but sadly I don't have the time to implement this. And if I eventually do, I can probably add exploration restrictions in just the PVP mode.

I'm just now going to be starting a run with this setup for the first time. I think Option2 would fit the theme better. Is there any way you can restrict getting in and out of vehicles do be done on/near a certain building? That might be a way to get past the issue of exiting a vehicle outside of the base.

There might be, but it's likely to be error prone (and being refused to leave a vehicle is likely quite annoying). Further you still have the issue that the vehicle may be destroyed, forcing you to leave (I'd say losing the game at this point wouldn't fit the scenario, you're sort of remote controlling the vehicles and not actually in them).

The exploration limitations is fine in the early game, but as I noticed in middle+ railworld games, it becomes more of a nuisance than a challenge.

I agree with you that option 2 fits the theme better, but it's fairly easy to abuse:
The exploration part is simply implemented. You can pan the camera as far north/west/south/east as you've scanned. However, this means that if you explore/scan diagonally (for example northeast and southwest), you'll be able to reveal unscanned sectors in northwest/southeast by just panning the camera. Coding a more sophisticated solution is difficult and will likely result in performance loss when panning the camera.
With option 2 you can just drive northeast/southwest to be able to reveal large areas without scanning/exploration. This is why I'm leaning more towards option 1, because it's so easy to bypass the limitation. The best solution may be option 2 plus a sophisticated model for preventing unscanned/unexplored chunks from being revealed by camera pan, but I'm not sure if this is feasible :\

I have one idea I might try out:
Basically "tag" chunks you're allowed to pan the camera over when not in a vehicle. Chunks get tagged when vehicle you're in drives into the chunk or a radar scans the chunk (sort of. you can't tag the outermost chunks as panning the camera to these chunks will reveal neighbouring chunks).
If I can get this working it'll likely have insignificant impact on performance, although it'll probably take a while before I have the time to try this.

I believe I've found an acceptable solution, so it'll be alternative 2. It should be backwards compatible with existing games (you'll still have to modify your savegame, as explained in the "Information" tab on this mod page).
I'll likely upload a new version within some hours.

You're right. The actual exploration is nice in early game, but becomes a bit annoying when you progress in the game. But I don't agree with Alternative 1, it would make everything too easy and break the mod.
My idea (I didn't try it untill now but I think it could be a good solution, going to test it on a new game) is to use a radar mod that would expand the radar area with research upgrades. Like this one for example : https://mods.factorio.com/mod/Big_Brother
Maybe you could think about this kind of solution, better than simply removing the radar expansion.

I went for alternative 2 and found a (much better) way to prevent exploration when outside a vehicle. I feel this is a good solution, so give it a go :)

One way to explore is by artillery. Perhaps an 'exploration drone' could be added that would go to specific points on the map, but still be able to be attacked by biters. It would be side-by-side on the tech tree with construction robots and require all the same things they do. You might start with 1 or 2 of them. Maybe make them require extra batteries or something to construct so they had a longer range. If they run out of power, they automatically limp home like the other robots do.