What powers on your Rune Priest? I'd recommend Living Lightning and Murderous Hurricane, and you can swap one of 'em out for Divination or something if you feel you need it.
Sticking out with the Meltaguns? To be frank, even in 5th edition I preferred Plasma over Melta when Footslogging Grey Hunters around the board. You'll rarely, if ever, get within 6" for the Melta to count and I generally found Strength 7 to be ample for dealing with AV11/12 (even 13 in a pinch and since I bring so much of it).
I don't like anything about your allied Guard detachment. Honestly, I'm not big on Allies at all at 1500 points or less and would be surprised if you faced two flyers on a regular basis at that point level. I can see you wanting the Vendetta though. Its probably one of the best anti-air units in the game right now. The rest of the choices are a little strange however.
Why the Leman Russ Executioners? At 1500 points I'd personally rather just take Battle Tanks and shave a few points off the unit. 2+ Saves are going to need to be dealt with, but two large pie-plates will do the job just fine, even in bigger point games. Personally I'd drop them entirely.
Why the Veteran Squad, and why not have fun with it if you are going to do that? For example
Veteran Squad: Catachan's Devils (180 points)
Gunnery Sergeant Harker (FNP, Relentless) w/ Flak armor, Close-combat weapon, Frag and Krak grenades, Meltabombs, 'Payback' (Heavy Bolter)
Veteran Weapons Team (1) w/ Flak armor, Close-combat Weapon, Frag and Krak Grenades, Meltabombs, Autocannon
Veteran (3) w/ Flak armor, Close-combat Weapon, Frag and Krak Grenades, Meltabombs, Sniper Rifle
Veteran (1) w/ Flak armor, Close-combat Weapon, Frag and Krak Grenades, Meltabombs, Demolition Charge
Veteran (3) w/ Flak armor, Close-combat Weapon, Frag and Krak Grenades, Meltabombs, Lasgun
Special Rules: Infiltrate, Stealth, Move Through Cover
That's quite a lot of firepower jamb-packed into one little squad. Even better, you can probably set them up in the Aegis Defense Line thanks to Infiltrate. Better still, is having Stealth to improve the cover save offered by the
ADL.
Too expensive? Drop the Demolitions Doctrine. 150 points is not bad for that much firepower, even without the Demo charge.
You can even keep the Catachan theme going and add in Guardsman Marbo as the Elite choice. 65 points is cheap, especially if you cut out those Leman Russ tanks.
Heck, you ever just consider an Infantry Platoon for the mandatory troop choice? You can bring oodles of Autocannons then. Put enough S7 shots out there that you are bound to get a few 6's (especially if you have a senior officer twin-linking the shots!).
Really though, you need to think about how your Army as a whole will function with both the Primary and Allied detachment. If you have some solid
IG troops backing you up, you want to be able to quickly deliver your Grey Hunters down the throat of the enemy. They're your shock troops. Use your Guardsmen to hold your home objectives.