I've been doing some work on this game for a non-TAS speedrun, and I figured I'd post some of the things that I discovered in case some of this information is useful for whoever eventually comes along and picks up this project.
In addition to the beggar counter, blood counter, and meditation counter, there are at least 2 other counters that work similarly: A counter for accepting half-price (or less) when selling an item, and a counter for giving the proper amount of money (or more) to the blind Herb salesman. Both counters are 16 steps and will only run down in the overworld. Both will give you +4 honesty, +4 justice, +2 honor, +1 humility. There is no counter for cheating the weapon/armor or the herb salesman (-2 honesty, -2 justice, -2 honor, -1 humility) so you will lose these virtues every single time you do it.
I believe party members will only join you if your virtue in their particular area is 40 or higher. The WIP TASes in this thread are just single-character, but in case somebody decides to grab party members for purposes of selling off their equipment this information may come in handy (paladin, ranger, and fighter being the most lucrative).
Chests in the dungeon will respawn if you enter a stone room. I saw it mentioned above that they'll respawn when you exit the dungeon or when you enter a key-room, but i didn't see stone rooms mentioned. The stone room is potentially more exploitable than the other two respawn methods. For example, in Shame you can hit the treasure room twice without any extra encounters beyond what you'd have to do anyway (assuming you're coming in and out of the dungeon from the bottom floor) since you pass the treasure room on the way up to the stone and then again on the way back down. Despise is the same way. There are also some really short loops that can be exploited to gain treasure fast. In Destard you can go back and forth between the stone room and the treasure room on level 4 with only 2 short encounters each time. In Covetus you can also go between the stone room and the two level 5 treasure rooms with just 2 encounters each time (the two encounters on level 7 only need to be done in one direction but not the other, since there is a one-way staircase from 6 to 7). Despise also has just 2 encounters in the loop, though there isn't a heck of a lot of treasure here so I'd probably not hit this one repeatedly.
Not sure if it's helpful, but it's worth pointing out that avatarhood in a particular virtue is indicated by setting the virtue counter to 100. Normally the virtue counter is capped at 99, then when you meditate for avatarhood you get bumped up that 1 extra point. So if you could somehow circumvent the code that caps you at 99, you could maybe gain avatarhood without needing the rune or the shrine-visit. I haven't investigated this (it's probably just a pipe dream) but it's at least worth somebody taking a look at simply because the potential time savings is huge if the game could be broken in this regard. For starters, I'd recommending finding all the characters and actions that raise virtues and using each of them while your virtue is at 99 just to see if any of them fail to enforce the cap. Also worth testing if the low-end cap is broken anywhere (doing all the stuff that lowers virtue when you're already at 0), in an attempt to get a wrap-around. Food for thought.