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Still very interested in #3 above.  Or if anyone has any expertise they would like to share on any of the 3 questions in my original post, it would be much appreciated!

EGOL - Wow - thank you for your thoughtful insights and experience.  That totally makes sense!

EDIT: the rest of this post probably incorrectly assumes my disavow file (submitted on March 11th) was responsible for my ranking and traffic gains since March 11th.  I am now reading a big algo change happened on March 12th -which I guess is more likely to be the cause of my increases /EDIT

I can definitively say that linking keywords in PDF's does hold some sort of detrimental effect on ranking - it has been a slow drain for many years.  Over the years, we have been unable to say - "Hey, we just got hit by penguin", because the downtick on algo change days was so minor compared to everyone else - almost unnoticeable - but the trend downward over the years is very, very clear.  SO we have always tried following the Google mantra, "make your site content better" - and we did, many times over, and for many years.  In my opinion, we  demonstrably and undeniably better content then those beating us in the ranking, so we could never figure out what was holding us down (I have not been that into SEO -just trying to make better content , unsucessfully, to fix things!), but I saw a tweet from John Meuller a few days ago that said people shouldn't link back to their site in widgets they produce - and so I submitted my first 800 links on March 11th to disavow.  On March 13th, we got several of our big rankings back (5th spot back to 1st in a few instances) and about 30% more daily traffic so far (or about 20,000 pageviews daily) - so now we know we initially made a mistake with those links.

Now, we simply didn't know the best way to correct things going forward, so I think your plan makes total sense. I really appreciate the time you took to answer my question!

Sorry for the long description above, I just wanted to leave specifics it in case some other poor sap is having similar issues as I did.

I have a few questions. My website allows people to create custom 'puzzle' and education (i.e. "math") worksheets -  enter your 'school spelling list' - I can make a crossword or many other puzzles (PDF form) from it. I recently realized that I was being penalized for the backlink I placed in each one. I placed in each PDF ("Created with mydomain.com Crossword maker") - I was linking the "crossword maker" back to my site. BAD!  I am now aware of this.  I have recently disavowed several hundred backlinks where people have posted those PDF's online - and have started to see a big recovery in ranking and traffic.

My questions about my citation: "Created with mydomain.com Crossword maker":
1. Moving forward, can I leave the same citation on each PDF - but just link 'mydomain.com' back to my domain (not the keywords, just the domain)
2. If not, can I just leave the unlinked text on the PDF: i.e. "Created with mydomain.com Crossword maker" -no embeded links at all.
3. Is it OK to assert that they must leave the "citation" (linked/unlinked?) to post them on their website as a part of my terms of use? If not, is there an acceptable way to get credit for giving away free custom content - other than asking for an 'optional' link back?

I have thousands more of these that I would need to end up disavowing so knowing exactly what is permissible is extremely important to me moving forward.

I have watched this whiteboard Friday: https://moz.com/blog/backlinks-maximize-benefits-avoid-problems-whiteboard-friday (I am looking for clarification on what I can put in the original content I essentially syndicate - the content is different on each and every PDF, except for the citation).

Thank you so much for your time and help!