Found another quest I can do - The Restless Souls (parts 1 and 2). I missed it earlier, and one Wowhead comment says even non-stealthers can solo this at level 59, all you have to do is wait for Restless Souls to wander close to the entrance.
Even though it's a "gun", it's a channeled weapon that frees up their souls, so it's OK (and my gun skill didn't go up, since players who can't use guns can use this).
Reinisch was also able to buy Captain Sanders' Treasure Map in the auction house, so now he too wears his shirt. Quest was already gray, so only 10% XP.
Update: I managed to do some more older quests: Tomb of the Lightbringer (a couple of Alliance helped, unasked)
I also read that it's possible to do Broodling Essence and get the essences even if the Broodling is tagged and killed by someone else, so I was able to do this by following people in stealth and using the quest item during their fights. Most of my essences came from an Orc hunter who waved at me but acted like a bot.
Broodling Essence (unfortunately, it just went gray at 63, 10% XP)
Felnok Steelspring (green, only 775 XP or so)