@Oliver De Ausen, you can absolutely do it yourself. But first, unless your lender requires the Quitclaim Deed (which would be odd), why not use a Warranty Deed? The Quitclaim deed has historically been the default for LLC transfer, but that was before the rules changed in our favor.
To get the correct verbiage for your deed, can you use the previously recorded deed for your subject property as your template? From there, just modify the appropriate sections, such as Grantor/Grantee, dollar amount/consideration, and potentially the lender/servicer if your loan was transferred.
Here's a good tip: newer Microsoft Word (2013 and beyond, I think) can open up PDF's and automatically converts them to editable text. If you have a PDF of a deed, try opening it in Word. If it works, review it carefully since the character recognition isn't perfect, especially if the source PDF is angled/tilted or a poor quality copy. I have Word for Office 365 and it opens PDF's fine. Worst case, type it out yourself in Word or similar; it's only 1-2 pages and won't take long.
Then, since it sounds like the lender is on-board, you could send them the unsigned draft deed for review, or to a Title Co or real-estate attorney (local or here on BP). I say 'unsigned' because a signed deed could be binding in your state, even without being recorded. Getting the unsigned deed blessed isn't strictly required, but strongly encouraged on your first go-round of DIY deed-ing.
On the other hand, since this will be your first time, spending the couple hundred dollars on a lawyer-authored deed could give you some piece of mind. You can always use that as your template for future use.
Once you've got your deed, just follow your county's procedures for recording. In counties I've been to, they require the original notarized doc, ~$30 for 2 pages, and it's recorded immediately if you go in-person. It takes me longer to park than complete the recording.