So...
I spoke to UKVI and the contact said to just put a cover letter in explaining why the middle name is different. She said it's important for the passport to be in the correct name (for what i submit) than the BRP. She said a cover letter will explain and 'you'll be fine'. She obviously said she's not a case worker but her usual queries are in regards to the passport being in the wrong name to what they want on the certificate and compared to the BRP. The way round I have it is easier to deal with.
Then I called medivisas and he was very blunt in his explanation. He said that I'll also be fine providing I put a cover letter. The majority of his conversation, however, was why am I even bothering? Just apply as is now and put up with the letter. If it bothers me that much I could change the passport in the future.
I'm not sure how I feel applying with the middle name as the initial. I like things clean and streamlined.