I'm already leveled up, with only a couple quests left: Arcomage (all I can do at this point); the obelisks (same); the last of the statuettes (same); and retrieve Halder's remains from The Maze only level 26 w/o GM Protection from Magic). Town Portal to Tularea does not trigger the Trumpet quest, and to Harmondale does not tell me Judge Grey is dead. I.e., there is literally nothing for me to do. How do I speed things up? I've never had this happen before.

If all you care about is passing game time with a minimum of real life time, then find a 5 day border between Tularean Forest and some other region and just cross back and forth until the Trumpet quest triggers. Don't worry about food; your characters will become weak when they run out, but no other negative happens. You can Town Portal to Harmondale and rest in your castle for free to remove the weakness. Harmondale is a great choice for this, since you should get the notice about the Judge if you have managed to miss the Trumpet quest somehow.

Beyond that, start working on quests you haven't received yet.

-If you are planning to choose Judge Fairweather, then make Arena runs for your 5 Knight victories. Get a Horseman henchman (the one that reduces stable travel time by two days) and you get hit the Arena on Sunday, get back by Friday or so, wait a night or two, and then it is Sunday and off to the Arena again. This will take about 5 weeks, which will probably put the trumpet in your range. You can check Tularean Forest between each Arena trip.

-If you're going with Fairweather, then you could also start clearing the Mercenary Guild in Tatalia.

-If you're planning to choose Judge Sleen, then make a point of picking up those Town Hall bounties, since they take a while.

-If you're going with Sleen, then start clearing out the School of Magic, if you already finished the Wizard promotion.

-Keep the Minotaur Kings at range and you can clear the Maze via kiting. Once you've cleared out the groups near the entrance, you should have enough room to shoot and retreat until the minotaurs die, which each newly dead group increasing the space you have to work with. TP to Harmondale for a temple trip to regen mana if you need to (or sleep at your castle for free).

-Someone on this subforum vouches for Rock Blast as a great way for dealing with Titans in the Titan Stronghold. Be careful, of course. If you're successful, then there is great loot to be had and the way to the Perfect Bow will be cleared for later.

-You could also start working on clearing some other dungeons that you don't have quests for yet. If you're strong enough, then Mount Thunderfist should have some good loot.

-Clear out the Vampire Cellar in Tatalia. The loot and XP make this worthwhile regardless of your choice for judge.

-Make a trip out to Evenmorn Island. There's too much loot to carry out in one trip, and several Master level skill teachers are there if you need them. Diamond Gargoyles might be a pain, but most of the rest of it should be doable, including both temples.

-If you are willing to take your chances, make good use of Invisibility, and are both careful and lucky, then you can try making the run through the Tunnels to Eofol to Land of the Giants and open up the Harmondale/Land of Giants teleporter.

I love rock blast for the Titans. Bounce them and they can hit around corners. The Insta-kill doesn't work if they can't see you. (They may get you once in a while so don't hesitate to leg it if necessary).
Or bounce them against the floor and you can hit Titans while standing in the green. The Titans don't know to come at you. Dragons a little trickier but not much. And yes. The loot is amazing.

I thought one needed to officially obtain the Quest before they would count. Then again, I play Light slightly more than Dark (this is going to be a "dark" game), so I may have missed that. I know it's not required for the Arcomage quest. I did clear out Thunderfist fairly easily, despite the absence of GM ProtMagic.

Anyway, after Thunderfist I leveled up two levels just to pass the time, and it turns out I completely missed the Trumpet quest (which happens to me more often than not), but at least I'm moving forward, now.

I think most quests are state-based. The Champion upgrade just checks the same variable your Awards screen uses to see whether you've ever gotten 5 Knight victories. The Bounty Hunter upgrade checks your current bounty collection total, and so on. I expect you can clear out the Haunted Mansion without the quest, then get it and immediately turn it in, etc.

Some quests require you to have the quest before you can get started (hard to place the statutes if you don't have the statutes, Wromthrax might not be around until you've gotten the quest, and I believe the Perfect Bow isn't placed until after you get the quest), but you can meet the requirements for a number of quests before you actually get the quest.

and five lord victories won't count even though higher. The game means five knight victories.

Lord victories not counting towards Champion promotion: isn't that one of the things Grayface patch fixed?

That I don't know.
Boy was I, ah, unhappy when I found that my Lords victories did not count. LOL.

Update: Did a couple weeks of training, after which Judge Grey died, so I missed the Trumpet quest again... :(

Train one week at a time (each characters gets one level per trip to training center), then teleport over to check between each round of training. I don't think you use any extra time training one level for the party at a time as opposed to training multiple levels at once.

In retrospect, I should have done that. I'll give it a shot next time, if I remember.