Just a few conceptual points:
For two years I've been working on drafts of a paper. I'm happy to
keep incorporating new sources and improving the paper, because the
topic is fascinating
This is a debatable action because it can delays your publication rhythm. For every paper, lay out the hypotheses, research questions, or objectives clearly and then work on the piece. Once the conclusion answers the questions, either seek feedback or submit it. New findings are going to emerge constantly and if one "keeps incorporating" new sources the paper will never leave.
In very rare occasions, one may want to add some new thing. For instance, by chance a very relevant paper was published during the composition of the final draft. To improve the relevance of the paper it'd be good to include that new work in the right section. Otherwise, there needs to be an end date in sight.
However, when I print the current draft out to look over after making
edits, I can barely read a paragraph before my eyes glaze over and I
This is not abnormal because you have read this multiple times and no new stimulation is coming out. Here are some ways to work through it:
- Circulate it among peers for a round of proof reading. Pay them with something: pizza, chocolate, a favor, etc. Consider forming a writing club, in which everyone can circulate works in different stages of development.
- Hire an editor, preferably knowledgeable in your area, to proof read it.
- Put this project down and work on some others, return to it again when you're ready.
- Read it out loud. It's actually very helpful because reading out loud lets you hear the rhythm of the words and this helps isolating clunky parts in the paper.
- Read it from the back. Start from the paragraph, and can also consider start from the last sentence and working its way up. This technique breaks the contextual flow and allows you pay more attention to missing words or typos, etc.
I wouldn't expect anyone else to read something that I can't, which
makes me reluctant to seek feedback
Why not? This is one of the mind blocks that scares a lot of writers. You don't need to share only perfect works. When you circulate the piece, just be sure to:
- State what this article is for and what stage it is in: is this a draft, a revised and resubmit version, a grant proposal, etc.
- Be very specific on what kind of advice you seek: for more drafty work you can ask for comments on overall big picture and structure. For more developed work you can ask for comments on prose clarity and wording. For final draft you can ask for proof reading level comments.
Overall, as a comment has pointed out there are some conflicting thoughts within your question and I'd just humbly advise you to let the security issue go and be open to criticism and comments. Your writing is not the entire you; no need to shy away from people's criticism. After all, writing is about communicating ideas and it's better to get early and frank inputs from peers and friends now than from the reviewers with the rejection letter.