Personally, I would fill out the form as well. Just so you have your bases covered, but if the sea time forms are on company letter head and complies will reg, you should be good. You can email NMC and ask for sea time letter requirements (from a company), and compare that to what you have, and staple a copy of that email response to the sea time letters - provided the letters you have comply.
Watch-out about estimating days, you have to be exact…and don’t say you have 31 days of sea-time in a month, like February. REDFLAG.
…and yes, OS to AB is an upgrade, and will require new physical and drug screens. Your local REC will help complete your application.