I do have an ICS cable and have changed the settings on my MR03, MR02 and F1. I don't use a brushless car, just ran one before. My track is too small for the brushless but, the small track size means we don't really break many parts. You can get other brushless motors from 4200 -12,000kv. A big track is hard on these little cars. Broke quite a few parts on the 1/18th scale carpet track using an Atomic 17mm 35T motor going wide open, pretty much modified pancar.
We don't run gear diffs anymore but, we did some box stock racing in the past so, I'll share my top secret setup, lol. The grease works but as you said it will work its way out and make a mess on the track. The stock springs on the damper from your LM car is the perfect fit for inside the gear diff (if they haven't changed anything since I last had one). The spring will force the outside of the diff against the tiny e clip holding it together and then the wheel nut will push the rim against this same part allowing for adjustment. Or just buy the adjustable gear diff made by PN but honestly, a ball diff is so much better.
The LP500 is a 90mm RM body and as I recall you can't run a top shock without cutting a hole in the body, I'm not sure if a disc damper will fit.
This might help you: http://mini-z-guide.com/
I'm not sure if it's still being updated but, there is still tons of good info.
Edit:It seems to be updated somewhat as they mention the Audi R8 as a current racing body choice and it's not that old of a body.