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cadians or valhallans
3 company commander
1 psyker primaris "old bleedin eyes"
1 lord commisars "Fistulus" with a powerfist and bolt pistol
1 Lord Castellan Creed (if cadian) or a 55 point inquisitor psyker (if valhallan)
230. Depending on who you pick as warlord, this pile generates at least 9 orders a turn, has command for 3 battalions, and one psyk/deny. (3 fewer, of course, without creed).

3 platoon commander
3 command squad with 2 grenade and 1 missle launcher each
3 veteran squad with 3 grenade and 1 missle launcher each
2 astropath with 1 laspistol each
457 (687 so far) 15 grenade and 6 missle launcher at bs 3, also 21 lasguns and 3 laspistol

18 squads missle grenadier regular gaurd infantry.
1044 (1731so far) +18 missle launcher and + 18 grenade laucher and +126 lasguns and + 18 laspistol

3 heavy weapon squads with 9 missle launchers at bs 4
189 (1920 so far) + 9 missle launcher. This gives you (on the incredibly unlikely chance you shoot first) 33 missle and 33 grenade and 147 lasgun and 21 laspistol shots, not counting the 9 or so from characters and 3 bolter pistol shots.

ministerium priest with poweraxe (index) 40
2 commisar elite slot with powersword and bolt pistol, each. (40)
= 2000 points.

An intriguing possibility is downgrading the two poweraxes to be chainswords, and running an el cheapo inquisitor psyker instead of a 46 point psyker. It would permit him a bolter rifle and chainsword.
To make this army downright terrifying, run it as valhallan (that loses creed, sadly) and substitute for him a second inquisitor psyker with chainsword and laspistol. The ability to get stuck in in melee without overwatch, or to mess up a big opponents firing, are nice. Traditional gaurd psyker spells other than smite are basically useless,

Advantages.
Quantity has a quality all its own.
Decent anti-horde.
Strangely immune to bad touching.

Love it,
Have you tried it out? If so how did it run?
Valhallan is my second fravourite regiment after Dkok. Balls are so big need a long coat to cover them.
Also they lose less guys to moral so are great at holding objectives longer and their damage doesbt drop off as fast. Not to mention as you said, better in melee than cadians.

I have just recently gotten enough individual soldiers to put it together, although they aren't all the same color paint. So, no, I haven't gotten to run it yet.
(I even have to proxy a couple squads with my elysians as "blue and white valhallans" .. and of course they donate the heavy weapon squads to be "elite ice warrior missle launchers."

Just as soon as thanksgiving is over (and as soon as I can get all my troops on packing tape movement trays so it doesn't take a year to deploy) I will get to try it out. It has been a long time building all those HWS's.
Valhallans are AWESOME in melee. They give "fire on my position" a new name, when you have 30 or so units that can fire krak or frag to give the order to fire into melee to. No army in the game can easily kill that capability, unless they snipe every officer I own. I reckon few in the game are hoping to try to cut their way through all the gaurd while that happens each round. (+ 2 smites and a malstrom from various psykers. elite infantry beware, the GAURD cometh.)

I sort of don't care how it goes, its my best 40k joke ever, just to put them all on the table and go "ok, NOW I am ready, lets see if I steal."

Con:
-Deployment, movment and shooting phase now last 1 hour each

Ack! Points changes to missle launchers!
Must .. recalculate entire list ...
(Also FIND it. I put so much stuff away when cleaning my living room that I now suspect my after family warhammer list may take a month just to FIND all the squads. Sheesh.)

Apparently the 15 point missle launchers going to 10 points saves this list some 330 points, which is borderline insanity. Its not just viable, its in strong need of a couple of brigades rather than 3 heavy battalions. It means the list can spam missle launcher sentinals again, which is a rabbit hole! I suppose three such doesn't kill the theme too badly.

But means that I have to buy more missle launchers again. Dear. God.

Edit. Whoops. saves it a mere 165 points on missle launchers. Enough to buy a mere 3 more squad worth, or 4 measley sentinals with 4 measley missle launchers.

So its a 37 missle / 33 grenade list. Ish.