I would try to cross sell on the bad PDFs. Ask the user if conversion went well; if they say so, direct them to Fiverr with an affiliate link.
We regularly perform PDF extractions at my startup. For each new client, we'll run batches of several thousand at a time.
A more attractive monetization model for a customer like us would be $0.01-0.03/conversion ($100-$300 per 10,000). A low per-conversion cost would easily allow us to test for a given group of PDFs if the conversion service was a good candidate for that batch, and if not, chose an alternative up-front (but allow us to test again the next batch easily at low cost). Also with a low start-up cost, its much easier to tell customers you won't make any specific fixes (take it or leave it, and test it first). Then you'd have the flexibility to work on broad classes of problems/improvements more at your leisure.
Ditch the free plan and make it a subscription service. Make it clear that some data can't be automatically extracted, and charge a per-page premium for manual extraction. If you don't want to do that work yourself, farm those jobs out to people on mechanical turk.
Sounds like a fairly niche product. Have you given any thought to that aspect? I've build a few too many products that are too niche. When eventually I woke up to that I just abandoned the projects. What's the point of building something for a handful of people.
Warning: I really don't know what I'm talking about.
I'd switch to having paid jobs only, but offer a money-back guarantee. Any users that take advantage of this offer too much could be turned away.
Who are your current users? If they are from a certain industry (real estate maybe) then try to target them and monetize off of that market.
The way I am reading this, even if you went paid you'd barely cover your costs (given how time consuming it is for you to bug fix). Plus without the free "trial" you'd struggle to attract paid customers, but while the paid "trial" exists people can just re-register to get all their files or otherwise only needed one page anyway so won't pay.
So my question is this: How much does running the service cost? If it is fairly inexpensive to run you could go a mixed "ad supported" and freemium model, with zero more bug fixes. Just sell what you have.
Instead of selling PDF conversion you sell convenience. You give your paid users an identical product but allow them to queue up dozens, even hundreds, of files via some basic desktop program maybe. Alternatively auto-magical conversion via email (PDF comes in, plain text goes out). Plus turn off ads (e.g. make free users wait 20 sec on an ad page).
The vast majority of your revenue would come from adverts, and while it might never be a screaming success, it might at least make a little profit year upon year and eventually pay for the effort you put into it.
But if it is expensive to run as is then I have nothing. You'll just have to try to make the paid model work.