I think you might be confusing the garnet gem that was in the fake Soulcaster and the garnet sphere that she was given by Kabsal for the disastrous portait. The sphere is the one that went dun, not the gem. So technically, Jasnah would still have been able to use the garnet in the fake Soulcaster, since the gem wasn't drained of its Stormlight. It doesn't say that Shallan noticed the garnet gem on the Soulcaster being dun, just that she noticed Kabsal's sphere being dun.
On a side note, the way I understand it, the gems and spheres are two separate items on Roshar. That is to say, you cannot just put a garnet sphere into a Soulcaster, because spheres are mostly glass and a tiny splitter of the denominating gem in the centre. The Soulcaster needs significantly larger gems, cut into specific shapes (in the case of the Soulcaster, oval).
So essentially, it wouldn't matter how much time had passed between Shallan's soulcasting and Jasnah's soulcasting of Shallan's blood in the hospital, although the time frame would most likely have been relatively small (maybe a day or so), in order for the garnet in the fake Soulcaster to still have enough Stormlight (regardless of whether Jasnah did or did not have Stormlight on her at the time). That being said, we know for a fact that Jasnah did have Stormlight on her, because she only shortly before saving Shallan soulcast both bread and jam.