Laser,Dr. B's "Diagnostic Hints and Treatment Guidelines" specifically discuss magnesium depletion, poor absorption via the oral route, and the frequent need for IM or IV supplementation in treating the symptoms and underlying condition of Lyme. These can be downloaded off of the ILADS website. His recommendation carry a lot of weight with many physicians who treat Lyme as a chronic illness. Showing one of yor providers these guidelines might help. A gram of IM magnesium every few days is quite safe. Much larger doses are used to treat pre-eclampsia and asthma attacks. If you have been being subtle in bringing this up, the docs may not realise that you actually want to try it. It seems to me that many of them have internalized patients' resitance to using needles and don't even really consider that option.
In my case, my doctor, whom I would describe as lyme friendly, had not used it but easily agreed based on that set of recommendations. In my case it helps a lot with muscle cramps and twitching. By the IM route, at any rate, magnesium sulfate is cheap, about a dollar per gram. I get it at CostCo. It's a 2 ml shot in the butt that does ache for several hours after being given. It can be safely given (IM) at home since the dose is low and (since it can also be given IV) inadvertent introduction into a blood vessel is not a big deal. However, if it does get into a blood vessel, it has a brief side effect of causing a sensation of intense warmth all over the body. It's brief and harmless but disconcerting if unexpected.
Some people have gottem naturopaths to prescribe magnesium and I don't know of a way to get it without precription. It doesn't seem to be carried on the European pharmacy websites.
You might want to post this question on "Medical" to see if others have comments or recommendations.
David