It's not possible that the device was drawing energy from other universes than the one it was presently in. To create a bridge between universes in the first place, they need an alternative source of zero point energy...
CARTER: Exactly. Yeah, we're hoping to use your proof as the theoretical basis for building a bridge from a parallel space time to ours.
JEANNIE: The energy you'd need would be enormous to the point of absurd.
McKAY: Absurd we can do. We have something called a Zero Point Module which essentially does what we're attempting on a smaller scale -- extract energy from subspace time.
This is also true of the process developed in "The Road Not Taken" to draw energy from multiple realities as the alt Carter was using the last bit of energy from the nearly depleted Proclarush ZPM to conduct her experiment.
The alt Daedalus, however, had no ZPM, and the capacitor was repeatedly drained to zero, so it could not be used to open a bridge after every jump. They therefore must have been drawing energy from whatever universe they were currently in. However, "The Road Not Taken" suggested that even drawing a microsecond worth of energy from individual universes could lead to a fallout of some sort:
Oh. Well our Major Carter found a way around that. She designed the machine so the bridge would only open for a microsecond. The idea was to steal small amounts of energy from thousands of different universes, thereby minimizing the fallout in any single one.
So rebuilding a capacitor that draws energy from their own universe is potentially risky, even if only used for a short period of time. It's possible that the people from the alt Daedalus didn't care because they were desperate and wanted to use the technology to steal ZPMs and other technology that they could reliably use in their universe, so they were not concerned if they caused problems by using the capacitor in other realities. On the other hand, we didn't see any fallout, so it could be that they solved the exotic particle problem. Good luck to McKay figuring out how they did that without having the device to reverse engineer or specs to study, though.
They could instead continue to pursue alt Carter's efforts to draw energy from multiple realities, but given Lee's statement that they were only minimizing the fallout, it's perhaps better to pursue technology that causes zero harm to other universes, especially for a group that has an abundance of ZPMs and is not in danger of immediately being destroyed.
One potential problem is that, if they successfully develop that technology and make long term use of it, there are going to be an untold number of universes that branch off from them that will likewise do the same. Over time, the number of universes stealing small bits of energy from other universes will grow exponentially and the likelihood that they would be drawing from the same realities, including each other's, will increase. I'd imagine the fallout from that would be fairly severe, especially since it wouldn't be easy for heavily impacted realities to contact all of them and tell them they need to stop before it's too late.