Good luck on BTA survival... not a good start adding it so soon, but it's there so check water very often and do regular changes.
6 mon to 1 year is generally the soonest advisable for 'nem addition. I added my first one at about 8 months... it's still with me 7 years later. If you treat them right they are easy, but it's also easy to kill them by rushing.
The "it cycled really fast" notion usually comes from people with prior freshwater experience. Saltwater is VERY different from fresh... This is an important lesson to learn if you don't want to just kill stuff left and right.
As far as the shrimp/BTA relationship... have you tried feeding the shrimp first?
Try getting something a bit tougher for it to chew on like a bit of squid tentacle, feed the shrimp a small piece of its food (they learn you are the treat provider pretty quickly and will usually start coming out to you to be fed). Feed the shrimp it's meaty bit as far as possible away from the BTA.
Then, feed the BTA a small meal of something meaty and very small (mysis) or finely chopped (I prefer a highly varied diet for mine, squid, scallop, shrimp, clam, mussel, ocean fish). It will usually slurp the meal down and the shrimp won't be bothering it.
My cleaners NEVER bother any of my 3 BTAs... could it be that the BTA is declining and the shrimp is interested in it for that reason?
You have a "crazy parasite" on what? What does it look like?
Lots of strange looking stuff hitchhikes in on LR, most of it is actually good. If you haven't positively identified it I wouldn't necessarily call it a parasite. If it's on your fish, it probably didn't come in on the rocks...