Q: Can reporters afford to pay you when they haven't gotten paid? 
A: Yes.

Consider their income.  What do they do, blow it at the racetrack every payday?  Squander it buying Hummels on eBay?  C'mon, they've got the bucks, if anybody does.  Reporters (at least the decent ones, anyway) have a good income.  They can afford to pay you, they just don't want to.  They, like most everyone else, want something for free.  Consider that you do their work initially without getting paid.  They don't pay you before you scope the job, right?  When you invoice them, you've already done the work, so why shouldn't you get paid?  So you invoice them when the job's done and when the payment hits the PayPal, THEN you send them the work YOU'VE ALREADY DONE.  What could be more fair than that?  If they squawk, you tell them that getting paid on time (or it looks like AT ALL in your case) is an issue and you're forced to do it that way.  You're not independently wealthy, right?  Explain it to them.  If they don't like it, tough.  You can let them roll all over you or you can get serious about earning an income here.  The best time to do this is from the get-go, then they don't have to unlearn their nasty habits.

How to make them pay way past due amounts:  Of course, this may drive off your business, but consider taking them to court for it (or threatening to do so).  If it's a court write-up, threaten to go to the judge about it.  Honestly, what would be more humiliating for a COURT REPORTER than to be taken to court for not paying their scopist?  You might even publish your policy on your website so there's no doubt what your payment policies are from the beginning.  Seriously, real businesses don't screw around about getting paid.  Basically you pay them first, then you get your product, right?

Don't let the amount owed you accrue up to several thousand dollars.  Invoice them long before it builds up to that level.  If you let it add up to that much, one, it's more difficult to get them to pay you a large sum of money like that; and two, it basically emboldens them and tells them you're a sucker that they can take advantage of.  I know it's hard to get tough if you've been "Ms. Nice Person" all along, but it's your livelihood we're talking about here.

Lastly, you might have to find yourself some new (and better) reporters.  Try to deal with intelligent, experienced, competent reporters, not flakes.  I know they may be hard to find, and I've run into more screwballs in this business than I can shake a stick at, even, believe it or not, one who used to run around in a Batman costume  and come into the office that way, who incidentially also used to dumpster-dive out behind the office building as well.  AND I'M NOT KIDDING!!!  You might try placing an ad in the NCRA magazine soliciting work from PROFESSIONAL reporters.

Post a policy on your website to the effect that you will accept work from professional level reporters only, NOT those who do everything with a tape backup and whose work requires literally filling in every other word from tape, who are just basically sitting there pretending to write down what is said while relying on the tape to pick up what they missed, which is probably at least 70%.  If you deal with those kinds of reporters, you'll get screwed every time.  Run your business like a REAL BUSINESS, not a hobby, and you might find things will work out better for you.  By the way, I used to be a stenotype reporter myself back in the '70s.

Josie,

If you know the reporting firm (if there was one) that your reporter got the job from, contact them and ask if they can assist you.  I had a slow payer one time.  When I mentioned to her I might contact the agency she worked for, she got real nervous and paid me pronto.

Pat