Note: This post has been edited to add headings, the level 4 dungeon chest information, and to correct the Fel Vesper bank reference.
PC, I think you stop gaining off GM-tinker crafted locked boxes at about 92 lockpicking. (95 just doesn't sound right, but perhaps it is.) After that you have to either go to Twisted Weald and do the discord thing or pick a bunch of Level 4 spawning chests. Trying to endlessly pick Level 5 or 6 chests doesn't work, although trying to pick slightly easier chests you have no hope of opening when your skill level is lower seems to give gains. Go figure.
Stratics has a nice guide to dungeon chests at
http://uo.stratics.com/thb/info/dungeon/dungeonguide.shtml . It even explains the difference between "static" and "spawning" chests.
Some of my favorite places to find Level 4 spawning chests are the south Trinsic bank in Fel, the chest area on the east side of Destard, the ogre lord island in lower level Despise, and the chests on the south end of the Yew crypts in Trammel. (See
http://uo.stratics.com/thb/info/dungeon/yewcrypts.shtml for a nice map of the Yew crypts. Also, I previously said Vesper bank but meant Trinsic. I found a note that said if the doors there are locked, try standing back about 4 tiles and use telekinesis spell on the doors.) Or attack a pile of level 4 chests that you've been stashing for a rainy day.
Level 4-6 Paragon Chests
The following paragons in Ilshenar drop Level 4 chests: Cyclops, Juka Mages, Liches, Meer Mages, Ophidian Avengers, Ophidian Knights-Errant, and Terathan Avengers.
These Ilshenar paragons drop Level 5 chests: Demons, Dragons, Efreets, Elder Gazers, Lich Lords, Sand Vortices, Serpentine Dragons, and Terathan Matriarchs.
And these Ilshenar paragons drop Level 6 chests: Ancient Wyrms, Balrons, Betrayers, Blood Elementals, Ethereal Warriors, Meer Eternals, Poison Elementals, Rotting Corpses, Skeletal Dragons, Succubi, and Titans.
I'm not sure what the levels are for some of the other newer monsters that drop chests (e.g., dark wisps), but I'm pretty sure they give at least Level 5 if not Level 6 chests.
Level 4 Dungeon Chest Locations
This is a list derived from the above-mentioned dungeon lockpicking guide on Stratics.
Covetous Dungeon - Water Ele room on Level 2. The boxes and barrels room on Level 3. The rotting corpse room on Level 4. East side of level 4 near staircase by the dragons and drakes.
Deceit Dungeon - Lich Lord room on Level 4.
Demon Temple - Room behind the steps and one outside it to the west.
Despise Dungeon - Ogre Lord island. Acid elemental spawn area.
Destard Dungeon - Throughout the big room on Level 1. Level 1 east side chest area. Level 2 close to the entrance. Level 3 ancient wyrm area.
Fire Dungeon - Level 2 near red NPC mages.
Hythloth Dungeon - Gargoyle and Demon room on Level 2. Five different rooms scattered around Level 3. Three rooms on Level 4.
Ice Dungeon - Arctic Ogre Lord spawn area close to ratmen and entrance. Both Arctic Ogre Lord spawn areas past the bridge. White Wyrm spawn area. At both the top of the stairs and at the bottom of the steps where the Ice fiends spawn.
Shame Dungeon - Level 3 poison elemental spawn area by the lake and building with the red mages. Some of the islands on Level 4.
Terathan Keep - Balron room on Level 2 and near the descending ladder (I think this is close to where the nightmare spawns).
Wind Dungeon - Dragon/drake spawn area.