I saw the post by EmielRegis saying he found no oil at all in his game. RSO did just the opposite for me. I was experiencing an oil-free game without it, with oil frequency low and size very small. I used that command he posted to uncover a large portion of the map and after meticulously checking every bit uncovered in a 3072x3072 area, I found there was not a single patch of oil on the map. But after installing RSO I began finding oil finally. At the same settings and same seed, I found one starter oil patch and two more within a 1024x1024 area.

I want to use this mod to save the game I've put more than 30 hours into, but I fear that once I find one oil patch, it'll be so rich I'll never need another patch again. Is there some way I can turn off the script that makes them get richer with distance? I want a game in which I must continue traveling and exploring to find new resources.

Making them richer for oil means that it will have a bit more % at start. Amount of oil wells per patch doesn't change that much with distance.

You can set richness_distance_factor to 0 - this will disable richness increase of patches. I would recommend agains this and I will be increasing base factor for next version. Once you start using lots of ores you really need those patches to be bigger or you will need to build outpost after outpost.

Maybe I should just set the factor lower than it is. I guess I travel a lot more than most players, and I build much smaller. I'll run across large sections of terrain, exploring and finding many resource patches. With default RSO settings, I feel like there's no reason to ever use trains because I can walk no more than a few dozen chunks and find a set of resource patches large and rich enough to play from start to finish. Often I'll see upwards of 300,000 units under one mining drill. That can take something like a week of straight playing to mine out. It's not just too much, it's WAY too much. Ratio-wise, it's like increase in time spent using the resources is thousands of times higher than the time spent exploring for new resources.

As the current richness and size exponents are 0.7 and 0.1, I am considering setting them to 0.007 and 0.02. If my math is right, I'll have to travel 75 times as far to experience the richness I'm seeing now. I could make that trip in one sitting.

From your description I would guess that you want to modify actual richness of patches. You can use those two:
starting_richness_mult, global_richness_mult

From your example I'd try setting them to 0.1 and not touching the exponents - those are only distance based and don't do that much till you go far out. You simply want to have less ore per patch - then richness multipliers are the way to go. Play with starting one so you have enough initial ores to prepare for long travel and trains and then adjust the global one to your liking.
You can use this command to quickly explore and survey larger area of map:
/c remote.call("RSO", "runTest", 2000, 2000)
Numbers are width and height of the uncovered area.

No, I wanted the amount of ores to stay about the same, but I like it going up slowly. I just explore so fast that I wind up having week plus ore patches in the first ten hours of play.

I was playing with the exponents and I discovered that at around 0.1 the amounts stay the same even at huge distances; any lower setting would actually cause resource concentrations to decrease! I am sticking with 0.35, which goes from about 600 per square to about 4000 per square when I move from the origin to 65536 spaces away. That's probably further than I'll ever travel, but I can go out there if I find myself really starved for resources. Mostly, though, I find that improvements in technology and infrastructure allow me to take better advantage of the same sized resources, so I get increased resource yield and land coverage over time even if the richness never goes up with distance.

I must say I really like how some patches are very large and sparse, while others are small and concentrated. Vanilla resource generation is (quite frustratingly) just the opposite--the largest patches have the most units per square. It is so bad that moving up one size setting often gives you as much or more per square than moving up one richness setting will.

All I need now is to alter the values for oil. I need it to be much less common than vanilla. I expect to do a good amount of searching to find a patch. I don't want to stumble across several oil patches just trying to find a single copper patch.

edit: I found the setting. I changed resourceconfigs\vanilla.lua oil allotment from 70 to 14.