"Can I get something that's a HUGE step up from the Jolida for $1500, or would I have to go higher for that to be a slam dunk?"
Nobody can answer that question for you Nolitan. Getting the best sound possible out of a system involves so many variables it's almost mind boggling. You might relocate your speakers and get the type of results your looking for. On that subject, matching your speakers with the correct amp is about as critical as it gets. If you want to play complex music, your amp must be able to provide power on demand, and some speakers are much more demanding than others.