Welcome to Fishlore.
Well, breeder boxes are pretty stressful and I wouldn't put a pregnant livebearer in one, as you saw. She'll stay pregnant, dropping fry about every 4 weeks until she runs out of stored sperm. But with a male in the tank, they'll all be pregnant their whole lives pretty much.
If you want more of the fry to survive, I'd recommend lots of hiding places: floating grass (real or fake) & lots of plants and caves in the tank give the fry places to dart to safety.
What I did with our platy tank was move the adults into a holding area.. another tank or big rubbermaid container (big enough they can swim around some and maybe put an air stone in it). Loosely cover the container so they can't jump out while you're working on the hunt for fry.
Then it's a matter of carefully pulling out the decor and substrate.. each to their own big container with some tank water in them (so any fry that hitch a ride out of the tank can have water and any good bacteria can have water too).
Yet another rubbermaid container is good to use for sucking debris out with a turkey baster (some fry will likely go for the ride here). Then you can suck out the fry that have no place left to hide. You'll need good lighting to check the debris for any fry that got into there.
For the fry, you'll want to setup a tank with a
bare bottom, just some caves and plants and either a sponge filter or a regular filter with fish net netting over the intake. (cut the netting off a small net and use a rubber band to secure it over the intake slots so fry don't get sucked in.)
Walmart or Target have storage containers about 15 quarts or so - we have about a dozen of these to use for fish tank work including fry removal and tank cleaning.