DMs are under no obligation to honor any undead created at a different table - as the DM has no way of verifying the players access to corpses; whether any undead were injured/destroyed; whether the PC lost control over any undead; etc. With so many factors that the DM has no way of verifying, the DM is free to say - you start the adventure with zero undead minions.
When it comes to resolving combats, it might be easier for the player to simply roll the attack rolls of their undead, and the DM to ask them to use average damage - as this would greatly speed up combat. If the DM is feeling generous, they can always allow players to roll damage if one of their minions rolls a crit, but I strongly recommend using average damage.
The player needs to be mindful not to hog the spotlight, and prevent other players from engaging enemies in melee. If it happens accidentally thats fine, but if the PC necromancer has so many undead that their turns take too long, and/or they are blocking other players from participating, the players and/or DM may see that as disruptive play.
Okay so let's break this down:
1. I've already stated that I'm looking for ways to
maximize efficiency at a table. Dice rolling apps pretty much solve the problem of rolling 16 d20s for at-advantage Skeleton Archers. I just give the lowest rolls until I hit, then damage totals. Boom, problem solved. Now if only someone would actually read the post I made and suggest such a dice rolling app that I can download to my phone or tablet....
Seriously, every concern you have is literally what I'm seeking advice for. Everyone immediately reacts without doing any reading comprehension because secretly they want to ban minionmancy. I'm literally going to the extent of buying skeleton minis with magnetic stackable tokens to eliminate hogging the table. What I'm seeking is advice to streamline the necromancer experience in an AL legal way.
2. Regarding not honoring undead created early. You're absolutely right. I, as a DM, also am under no obligation to honor literally anything on your character sheet that isn't class/background starting equipment or a magical item. Why? Because there are no rules for logging purchases like Plate armor, health potions, or purchased weapons. Every bow/crossbower user has 0 arrows as well. No one has mounts of any kind (unless certed of course because that what several DMs have said their policy is here).
Let's see what else doesn't get 'officially' recorded and thus DMs aren't required to carry over....
See how quickly that becomes absurd?
Even on the official adventurer's log there is a
Notes section. So simply have players record spell effects in that
Notes section and poof, problem solved. Drop a bajillion gold on making a Secret Chest (which I know you've done) or a Clone? You get treated the same as someone that drops 1,500gp on their set of Plate armor.
Honestly, this is the most
minor of concerns because within the first combat or two the problem will generally solve itself. Needs to be humanoid corpses/bones of course but that generally hasn't been a problem so far. If anything it's more of a spell slot management problem than anything else.
We've already gone over this earlier in the thread. AL should either put out explicit guidelines if DMs want to have such table variation (which is largely the purpose of AL, to reduce that when it becomes an issue ala restriction races, source books, spells, etc.), or inform DMs of the general guidelines for having multiple creatures under a player's control for longer than something like a conjuration spell.