landlord reference letter lackluster?

Hmm a bit lackluster but what are you expecting? A heartfelt letter? For your personal and professional reference letters, I just just searching for samples online, and then having your contacts read before writing to make it a bit more spirited.

Does the board application package specifically state that they require letterhead and a signature? If not, don't worry about it (I personally think it looks better if those things are there, but I'm not on your board).

It would not matter. All the board wants to know is that your paid your landlord and did not sue them etc in which case you would not have gotten the letter at all. Board is more likely to focus on your financials and wants to make sure that your are not a trouble maker.

Agree, it doesn't matter for the landlord letters, they just want to know you paid your rent. Plus, people are busy. It's different with personal and business reference letters, you should make sure those are good depending on how tough the listing agent says the board is.

Make sure your friends have an idea of what a good letter looks like, there are lots of samples online: https://www.hauseit.com/nyc-co-op-board-package-reference-letter-sample/

Some listing agents will make a big deal about making sure you include a personal story etc. Push your friends to speak up for you!