I hesitate to post on this subject as I'm biology challenged unlike a lot of folks here but thought I would mention something that has helped me recently. First let me say that folate heavy food causes serious sweating, insomnia, and inflammation in me. I have not taken a methylated form of a B vitamin since 2015. I would like to be able to eat salads again but am about ready to give up on that. Taking niacin and electrolytes helps with overmethylation but not a total solution for me. I still overmethylate and wish Dr. Lynch would quit saying, "Just take a little niacin, and everything will calm down." Sheesh.
While working with Bob Miller, the naturopath, with Tree of Life, he said to me that folate drives MTOR and can cause inflammation and excitotoxicity. Hmmm......
So after eating anything green I try and take some things that inhibit MTOR. Some things I might take - curcumin, valerian, olive leaf, magnolia bark, eldeberry, etc. I'm not saying it's magic but this has definitely helped me, and maybe this info can help someone else. Joe at Selfhacked.com has a great article about MTOR so I'm posting in case it's helpful. https://content.selfdecode.com/mtor-natural-mtor-inhibitors/
I'm also still in the process of figuring this all out so dont take my word as gospel, but for a long time last summer I was having very similar reactions to you to any foods containing folate.
For months I assumed it was overmethylation and tried in vain to calm things down with different forms of Niacin.
Eventually I figured out that it wasn't overmethylation but inflammation, and that it was caused because I was missing some essential cofactors that folate needs to work.
Specifically for me it was the other, non-methylated B-vitamins, so B1, B2, etc. These are just as essential for B12 and Folate (B9) to work and if you're missing any of these it can cause very intense reactions (see Ben Lynch's site for details, also some of the B12 guides on this site stress it).
Anyway I was not aware of this at the time and had been prescribed a supplement high in B12 and Folate by a nutritionist but which lacked all the other essential B vitamins.
As soon as I started a supplement with all the remaining B-vitamins I began to get considerably better. This might be something worth bearing in mind for you - if you try it make sure to take it with food.
There are other cofactors too, such as potassium and magnesium, that you might be missing. And deficiency in any cofactor will prevent your body properly methylating and will likely cause inflammation.
In fact this is what I'm trying now - adding different cofactors to see if it calms down my reaction - and in the past couple of days I've begun to have some moderate success. Specifically for me I've added a multimineral, Vitamins D, A, and a small amount of methyl-B12 and Folate.
The fact that the latter two don't seem to have worsened my symptoms would appear to suggest it's not overmethylation I'm dealing with after all. Perhaps something similar is going on with you.
Best of luck with how you get on.