Hopefully they'll let you do that, considering the hassle you've had. As you say, theres plenty of other things for them to work on in the mean time. Your email is very polite, so they would have to be total arseholes to say no.
If they refuse, then tell them you want reimbursing for the time/fuel etc of the additional journey...they may not give you cash, but could fill your car up for you whilst its there. Its not their problem that there is a distance involved, but this is one area where they could show some goodwill.
This whole "item on backorder" thing annoys me. I know there is nothing that can be done, but in my opinion its still BMW that are delaying things. (Similar to my seals...on back order for a while).
The whole thing just makes me think some dealers don't care about the customers once they have closed the deal. Its how a company puts things right that counts, and in our cases they are failing miserably.
Is this next visit the one that you said was their last chance, and if it comes back with more faults or unfixed issues then you're gonna reject it? Send any letters to the DP, BMW Customer Services and BMW Financial Services (if you're with them). BMW Customer Services will tell you to go to the dealer (which you will be doing), but I think its good to tell everyone! Make sure you've got a list of dates etc that things happened and the number of seperate visits and days its been in the dealer.
Of course, with any luck, they will have the car in and fix everything....