Originally Posted by kyselad
So here's the question: won't I throw the other adjustments way off by evening out the tension? And conversely, won't I be undoing all that tension work once I return to truing and dishing? Maybe there's some magic here that I'm missing that lets me handle truing and dishing without impacting tension much, but it's just not obvious to me.
If it was my wheel, I'd start the whole tensioning and trueing process over.
Loosen every spoke until you have just one thread showing. That will give you an equal starting place for each spoke. Then gradually build a little tension into the wheel by turning each nipple an equal number of turns. Don't be impatient. Two small tension adjustments are better than one big one.
While you are doing this, it's also important to work at getting the spoke heads seated in the hub - what many people call "destressing". I'm not sure how you do that with your goofy 3 leading and 3 trailing pattern.
After you get the tension to where you want it to be, true the wheel by making equal opposit adjustments to pairs of opposing spokes. That will true your wheel while making the least affect on the overall tension.