As you know I'm a big believer in detoxing as that helped me get better. But I'm not a doctor so I could only give you my opinions...
You asked about timing, I believe detoxing should be done every single day no matter what protocol a person is on, especially the detox baths and dry skin brushing.
When you say that after a sauna or lymph drainage treatment you get a strong reaction, that tells me that you are right, your body (and possibly brain) is filled with toxins. I wouldn't call it a herx but simply an overload of toxins.. The reason I say this is because those toxins could have been dead for a long time already and are just staying inside your body causing you problems.
My thinking is if you could stop all antibiotics for a while and just concentrate on doing the salt/peroxide baths (I know people who do them 3 times a day), that would be a good start, so maybe increase the baths...
If you are suffering from brain fog then I highly recommend Dr. Jernigan's Neuro-Antitox CNS/PNS Formula as that product really helped me and other people I know. Most toxins convert into ammonia and when a person has too much ammonia in their body that causes brain fog, joint pains, liver problems, and the list goes on.
As far as genetic problems with detoxing, I'm not sure I understand that.. For instance, when a person sweats that is a form of detoxing. Just like when I exercise, I sweat and I know that's a good thing. Can sweating or not sweating be genetic? I don't know..
Some detoxing is not pleasant and it is not designed to be pleasant, i.e., when a person first starts detox baths, they usually feel worse which is perfectly normal, their bodies are adjusting to ridding their bodies of toxins.. but if they stop they are not accomplishing anything.. just like exercise. Detox baths must be done on a daily basis. In Dr. J's book he has 3 different types of detox baths but I have only done one, the salt/peroxide one..
Have you tried internal cleansing? Like the gallbladder/liver cleanse? That's a healthy thing to do whether a person has lyme or not.
You mentioned laser treatments and I don't know what that is so if you could explain that to me I would be most interested.
On another note, that's great that you are drinking so much water and liquids, good for you!
I don't know if I helped you at all, I'm still drinking my first cup of coffee and not fully awake yet!
Hang in there,