Snazzy. I like the general concept, and you've got some neat stuff there. A few things that occur to me:
*As worded, your Ragnite Alloy Armour Plates not only prevent a weapon destroyed result, but also ignore the hull point that would have gone with it. Is that intentional? It would make fluff-sense to keep it as is, but I worry it might be a "feel bad" rule for your opponents. Especially considering this tank can be pretty well protected with its Conqueror doctrines.
*Specialty shells are cool. I feel like you'll be hitting with both shots more often than not even without
BS bonuses, but at your price point, that's probably not a bad thing.
*Unstable Power Cores. Awesome! I love rules that give models a weakness to exploit. That said, this tank doesn't have much motivation to *not* just stick its butt against a board edge, so this is really only going to come up in close combat. Which isn't necessarily a bad thing, but it seems like it would be more fun to have it moving up the field. "Okay, this thing's land raider tough on the front and sides, but if I can just line up that rear shot..."
Also, the Haywire thing is actually technically a debuff for some weapons despite being a huge buff for most things. Meltaguns, for instance, would be unable to get an Explodes! result against rear armor, and anything that would auto-glance or auto-pen AV12 is less effective as a result of the power cores rule. This is easily fixed by changing the wording to give your opponent the option to make their attacks haywire before or after rolling to hit.
* Doctrines. I'm not very familiar with how they work yet, but these do make me a little iffy. Before we get into mechanics though, let's talk names. Your "conqueror" rules are defensive, and your "protector" rules are offensive. Which sort of makes sense if you're using the tank as a siege device while conquering and protecting your fortresses by making your tanks aim better, but it still seemed a bit funny to me.
Now, mechanics. I'm mostly fine with your Protector rules. The rapid fire shells rule feels a bit strange on something that can be made to basically auto-hit, but I'm still fine with a shot getting super-sized consistently at the price point you've set for this thing.
The Conqueror rules are what have me a little worried. As mentioned previously, this tank doesn't really have much incentive to not hug the board edge/cover except that doing so might interfere with lining up shots. I know vehicles don't get cover as easily as monstrous creatures, but setting a skitarii walker between this guy and the enemy's best guns seems pretty easy. Thus, it's pretty easy to make this a 4HP tank with
AV 14 that downgrades pens to glances on its sides, and has a 3+ cover save on top of all that with a weakness you won't be able to take advantage of until you cross the entire board to reach it.
Beta doesn't seem as bad. You decrease your offense pretty significantly, but you can also get, say, a bunch of those walker tanks with the high strength blast a relatively good cover save through the use of cover/screening units. I like Beta.
I'm not as comfortable with Alpha. Alpha gives you a 4+ save out in the open on top of your other considerable defenses. Any amount of screening (say with a walker in front of you) makes that a 2+ cover save while still giving the walker at least a 4+ cover save. It does make your shooting much less scary, but anything that can hand out stealth and shrouded to everything around it makes me nervous. Could be cool to use in conjuction with scouting skitarii though. Run the rank up as fast as you can turn 1 to give a bunch of nearby infantry and striders 2+ and 4+ cover saves for a single turn. I'm not saying Alpha Conqueror is broken. I'm saying it makes me nervous. Someone more familiar with Doctrine rules would probably be less concerned than I am.
Overall, I think this is a great starting point for the tank's rules. I'm mostly worried about it ending up sitting in the back and shutting down most return fire with its cover saves and Ragnite Alloy Armour Plates while slinging nasty anti-tank shots around.
IHave you considered making the main gun actually behave like a rapid fire weapon? Obviously, just giving it the "rapid fire" weapon type doesn't work because tanks ignore that, but having a rule that makes it fire only a single shot at more than 21" gives you an incentive to move this tank up the table. You can still castle up with it and use it as a cover generator while slinging a single shot around if the situation calls for it, but you'll lose out on a lot of its offensive power.
By making it actually be "rapid fire," you give it a reason to roll up the table. Rolling up the table means it comes into range of more weapons that can brute force it to death, and it also increases the chances of something lining up a rear armor shot. This makes Protector more of a tough choice because your mobility might affect your ability to bring both shots to bare, and it makes Conqueror something that can bolster your forward forces rather than just giving you a frustrating castle of tanks in your backfield.
If you do make it "rapid fire," you could probably afford to up its range to 48" rather than 42".
