Thats unfortunate as now its just a guessing game people have spent hundreds and still been in the same position , id leave alignment till last it shouldn't cause a vibration more a pull or lean if anything and if you end up changing front suspension you will need to re-align again i had a very slight sticking caliper cause bad vibration too at one stage

Get it to a good mechanic (who knows the e39) and get him to give it a good look over i dont want to start recommending parts as it could be a waste of time