I take from your list is that you are using the 3 units of skellies to shoot/bog down the enemy and counter attack with Tomb Scorpions, Chariots and Tomb Guard? Is that a correct assumption? How's it working out for you?
Here's my take, ableit mostly with my 2250 list in mind. But the theme of it can be used with a 2k army.
I'm a big fan of Tomb King with Destroyer of Eternities and Collar of Shapesh. Have had great success with that. Possibility of 2-6 Automatic strength 7(or is it s6? I don't recall) hits with killing blow is pretty strong. Collar of Shapesh is essentially a 4+ ward save for 25 points.
Flail of Skulls is a pretty awesome Magic Weapon though, for my 2250
TK list I have it on my Tomb Prince. Definitely a must have item.
Liche Priests is the standard load out, which is what you have. Magic Defence all the way, you'll need it. I've beeng running my Hierophant with the cloak of dunes lately, just to make sure he's in the right spot to cast his incantations.
I can't remember off hand, but do
TK skellies come with Light Armour standard? If not I never find myself paying for it. Those points can be used elsewhere. I rarely take magic standards for the same reason, they are there to fight, die, get ressed, die again, etc etc until they break/wipe out their foe, or vice versa.
2 units of Archers, 20 strong, then 2 units of 4 chariots are my core choices. Maybe a swarm base or 2 if I have the points, just for kicks.
I sometimes use champs in my skellie units to challenge anything that threatens my Liche Priests. The champion will more then likely die, but no matter how bad he gets dominated, you can bring him back and challenge again next
CC phase, and your Liche Priest is still hopefully safe.
I use 4 chariots per unit, if they come in contact with terrain while you are moving, 1-2 will die but you can bring them back later.
No screaming skull catapult or Carrion? Carrion are in my humble opinion, the greatest warmachine killers in the game. You can sling shot them across the board on turn one.
Just 1 catapult can ruin someone's day when it works properly, plus the possibility of firing 2 times in a turn is pretty strong, although that increases the chances of misfire. Against low Leadership armies, it generally earns its points back. I use skulls of the foe against average Leadership armies, just to increase chances of panic.
I buy the reform banner for my Tomb Guard Unit, that banner allows them to basically control the area around them. They become suprisingly mobile with that banner.
Tomb Scorpions are awesome, I rarely use their underground deployment rules, I have them lurking behind my units and counter attack with them. They are stat wise on par with Tomb Princes, with poison, killing blow, special deployment rules, high movement(compared to the majority of
TK units), undead contruct rules. Just a great unit at a great points cost. I run 2 in my list as well.
Hope my take on a 2k-ish Tomb King list helps