Is it possible to change (increase) the distance between the resources of the starting field in the options?

There is no option for that. Currently they are just placed randomly but not that far away to ensure they are all nearby and fit within starting area (more or less). They might get further out if there are many of them and there would be a lot of overlap.
And whole thing is pretty much hardcoded right now.

Would love it if the resources weren't so close to each other

Can you be a bit more precise when saying they shouldn't be close?

They are being spawned randomly and making some distance guarantee between patches would make it overly complicated.
Giving more space to random placement could change something but it still won't guarantee that they won't be next to each other.

There is also a space limit of starting area size that I'd need to take into account.

Laying down a miner on iron that mines coal and iron clogs up my iron bus with coal and laying a coal miner clogs with iron. Filtering off produces gaps in the bus which unbalances. I do play with your max settings on size/richness but reduced frequency. If they were spread out a bit that would make your mod that much more enjoyable for me. It is mostly just the resources in the starting area that are troublesome due to beginning tech. Either way, thanks for your work on this mod. I enjoy it every game.

25% frequency, 600% size/richness
https://imgur.com/a/z0j28sv

Hmm looking at the map - I really need to start dividing resource size multiplier. Maybe compensate that in some other way.

Resource patches you have are larger then mod is prepared to handle properly. I think this started to happen after map resources overhaul in base game added ability to set higher multipliers.

I tried to change the starting area generation a bit but I don't see a good solution.

With 6x multiplier to resource size ore patches get so big that they will land on each other at least in some degree.
I tried to make collision avoidance to use 2 chunks but it leads to both slow performance and still doesn't prevent collisions. When your resource field is 5-6 chunks wide there is no good way to prevent overlaps especially in starting area that has by default radius of 3.5 chunks.