A couple things I see right away:
Priestly Breastplate doesn't work like Magic Charms - because it says "may be placed on" in the special ability instead of "may be activated on" in the identifier, it takes up your artifact slot on the turn you activate it. Also note that it negates Burning Incense (if you don't have Altar of Incense up, of course). Probably not worth it.
I see you only have five dominants - it's almost always worth it to run as many as you can. I'd recommend The Second Coming (or New Jerusalem if that's too expensive) and Burial (since you're running Lost Souls).
If you're running Disciples Aaron, you should probably throw Moses in as well. It's not as strong as it used to be with all the CBP stuff running around, but a 14/12 FBTN is pretty strong. He's also a second Judge for Eli's Sound Advice. There's also a case to be made for running the G deck version over CoW, especially in regard to your feasts.
Is your Eleazar the Priests version or the Persecuted Church version? I'd definitely recommend PC over Pi.
I like the idea of Ahimelech recurring King Saul's Spear, but it's probably one of the weaker links of the deck.
You really should be running Phineas, son of Eleazar, if for no other reason than making Zeal CBN. On that note, even though he's Z's Temple, Joshua the High Priest just makes all his enhancements CBN and can be pulled by (PC) Eleazar, so I'd run him as well. Every Tribe is also fun - he works off Melchizedek!
Temple Dedication doesn't do much for you - unless you call Dutiful Priest a Solomon's Temple priest (which means he can't trigger Tabernacle, Aaron's Staff, or Eleazar), it basically just reads "Search deck for a Temple Artifact." I would drop it.
I don't think most of the offerings are worth it. Note that Burnt and Guilt don't negate, they just discard. I would drop Burnt, Guilt, and Altar of Burnt Offering. I would probably also drop Fellowship Offering - Jehoiada's Strength and Not Alone are more or less direct upgrades. Even Grain Offering is mostly good off Dutiful Priest, and most of the time you'd rather be playing G&O off him instead.
Because Tabernacle Priests don't count as Temple Priests, His Name is John is pretty bad in this deck. Again, the only use for it would be to select DP as Solomon's Temple.
Passover is really good sometimes and pretty terrible other times. I suppose it works as Tabernacle fodder, but better would probably be First Fruits.
On the defense: You're going too many different directions. I'd recommend picking either grey or brown and building a defense based on that brigade.
I see that your reserve is entirely Tabernacle targets. While that's certainly one option, I'd recommend dropping at least a few of them (Inspection, Perpetual Priesthood, Phineas's Spear, and probably Melchizedek's Blessing and Jordan Interrupted) with some situational evil characters (Uzzah, Foreign Wives, Gomer) and adding The Deceiver to your main deck.
One recommendation that I've found useful in my Tabernacle deck: Seventh Seal can pull Trumpet Blast and Trumpet and Sword from reserve. I run both in my reserve, pull them with Seventh Seal, and if I don't need them I use them as the card from hand for Tabernacle.
I also like Eternal Covenant in this deck - it allows you to use a hero to pull enhancements from discard with Tabernacle, then get the hero back next turn.
