Thank you @
princess suki, and @
fabuleux for your responses. I didn't realize that even with a VAT refund, you get a portion of the VAT back (about 13 percent compared to 17 percent at Duty Free).
You can contact the airport boutique before you travel to see if they have it/can get it in. If they confirm I think you need to pay in full in advance. Not sure of the exact procedure because every time I’ve tried they couldn’t get what I wanted, but worth a go I think. Then if they can’t you still have the opportunity to purchase in Manchester or London.
This is exactly what I'm going to do. Since they don't reserve Speedys, I'm going to call and check inventory in the weeks and then days leading up to when I fly out. If the day before, it looks like inventory is low, I will buy in London and claim VAT back.
(Why not just buy in London automatically? Claiming the VAT back is a hassle I'd like to avoid, and also about a 50 USD difference. Yes, I'm getting a "discount" no matter what because of the price difference and VAT but I do like to be reasonably frugal-- that's how I save for my bags!

)
On the advice of a SA, I've also reserved a personal shopper. That way if my terminal's store does not have the bag I'm looking to purchase, but another terminal does, I can go to Louis Vuitton in the other terminal to collect.
I hope this is helpful for someone in the future that is looking to purchase at LV in Heathrow or London.