for people who love the littlest dairy goats
I'd be more concerned about parasites than bloat. Jess is right, if it were active bloat they would be critically ill by now. Leaves should not be hurting your goats, it's their natural diet. It's possible they got into some poisonous ones, but that wouldn't necessarily cause bloat. And that would be a completely different treatment plan.
Most vets don't know a lot about goats. I would call around to the large animal vets in your area and see if you can find one that knows goats.
What are you feeding them? (What is their normal diet?)
This is NOT bloat. They would have been dead long ago. Big belly is a classic sign of parasites. They're starving, so they're eating as much as they can. Pull down the eyelids. My guess is that they'll be white or very light pink. They should be dark pink or red. White means they are extremely anemic and could die at any time. That would also fit with lethargy. If you've ever been anemic, you know you don't feel like doing anything, including eating. This is VERY sad that your vet doesn't know this.
A fecal can confirm but NOT rule out parasites. If they said it was "negative," they may have simply messed up the test. Goats will ALWAYS have some worm eggs in their poop. It's an over-abundance of worms that will make them sick. You have to be sure that you use fresh poop and that the fecal is done immediately and correctly. Worm eggs will hatch in the poop if it's above 50 degrees. If it's room temp, they'll hatch in an hour or so, so if that sample sat on the counter in the vet office, they would not have seen any eggs because they'd all hatched, and they don't see live worms in the flotation. If your vet is used to seeing dogs and cats, they have "negative" fecals. Goats don't.
The way you tell the difference between "hay belly" and bloat is that with bloat, the belly is tight as a drum. With hay belly, when you mash it in, it stays mashed in for a bit like cookie dough because you're mashing in all of the chewed up hay and grass.