Juogi Tips?

Having one hell of a time even getting my alignments high enough to be able to even successfully finish this one. Any tips on how to keep my furnace intact long enough to finish this synth? I've been trying this alone and I've been close but the furnace runs out of HP before I can get the elements high enough.

grab another synergist and both work on it?

If you don't mind spending the fewel, I'd say get a clothcraft smock with the repair ability and spam heal the furnace for more time. Or if you can get a synergist with one, have them do it.