It's been a looong time since the first and only time I played through this game, and I remember I didn't even use the latest official patch back then for whatever reason, but now I wanted to have the best and most complete version possible, which it would seem the RP provides. So far it has been pretty good overall, no bugs or anything, but one thing is bugging me a bit:

Whenever I have a random encounter with Bandits or Slavers or just about any human and sometimes non-human enemies, there are always like 10 or 12, or even more of them per encounter, which not only makes the game quite difficult at times, but I also don't think it is very immersive to have the wastes just full of people like this - not even talking about the caves you sometimes come across (no idea if they also exist in the original game - edit, ok, they do) which are full of a single enemy type, including human ones. I am basically just ignoring those.

Anyway, I found this page : http://falloutmods.wikia.com/wiki/Editing_Random_Encounters_in_Fallout_2

It is explained how random encounters are put together by the game and I have compared this to the Worldmap.txt in my game. It looks pretty ok to me, with much more reasonable numbers like 2-5 or sometimes up to 8, but I ALWAYS seem to get these high numbers instead of them being randomized as they should.

Does anyone else have the same problem? Or any idea how to solve it? I am probably not going to start a new game, as far in the game as I already am, but it would be great it there was a way to fix this.

Never had this problem, OP.
Besides modifying the game files, other things you can do to decrease your game over frequency (as awesome as that narrator's voice is, it can get irritating seeing that screen, after a while) :
Recruit NPCs to eat bullets for you, just make sure to travel with some stimpacks (and try to not waste them if possible. Whenever you sleep using your Pip-Boy 2000, your followers will slowly restore HP too, not only you. Resting with Pip-Boy is impossible in some situations - while you're in combat / while exploring some areas in Vault City, etc).

Improve your outdoorsman skill. If you detect a group of enemies but you're not feeling confident (pack of Deathclaws for example), avoid the encounter (if you have high outdoorsman skill you'll frequently see a message asking if you wish to accept the encounter or not). Carrying a motion sensor (with the main character) will add 20% to outdoorsman, so try to find one.

Traveling with the Chrysalis (the car found in The Den) will help you to avoid encounters. You can purchase it from Smitty, or steal it (since you're playing with killap's RP). Since it's broken, you'll have to find a replacement part, first.

You can change game and combat difficulty in the options.

Change one of your traits to Jinxed and see some enemies exploding, while you laugh hysterically (be sure to save frequently, because the trait will affect your combat turns, too).
Jinxed is already good vs few enemies in my humble opinion. So if you're finding large groups (10-12 you said. That's large!) all the time while exploring, I believe you'll have great results using this trait, OP! Give it a try, if you can change a trait without ruining your character build.

Thanks for your answer. Yes, it got a lot better since I have the car, and outdoorsman skill helps, too. Also, my character and companions are strong enough for most encounters, so it's become a lot less frustrating.

savescumm before you travel to avoid them if necessary

Small update, I now know that the amount of enemies you face during random encounters is determined by your own party size, so when it says something like 2-5 in the Worldmap.txt, this is multiplied with the number of NPCs that accompany you. So with my party of three to four, it makes sense that I had these kinds of encounters. I also now read that Killap made it so that especially early on in the game, the wasteland really feels like a hostile place by making the encounters this tough.