"Related question: If a Soviet artillery division is not attached to the same Army HQ as the units it's supporting, does the attack get schwacked with the CV percentile decrease for attacks involving units from multiple HQs?"
From my experience the Arty does not seem to support units belonging to other HQ's, or at least I am not seeing such in the combat results. Still, I build mountains of them as soon as brigades are available, then Divs later in the war. The brigades are not very potent but a dozen of them do a great job of knocking German fort levels down by pre-bombardment. I have used them with much success in crossing major rivers like the Dniepr.. first moving the art forward, bombarding and then making way for units doing the actual cross river assault.
I attach them to the Airborne Hq's and use them like forts to keep rear area fortifications from crumbling while they are initially building up to TOE, then move them en-mass and use in their bombardment role as required. When their mission is complete they are pulled back again to rebuild/supply. I never leave them near the front when not in use.. one attack against them and they are routed and useless for 5-6 weeks while they build up again!
I've also had luck in static situations where my artillery continuously bombards the same German static hexes turn after turn during the mud times, forcing the enemy to rotate units into the hex at an increased rate in an effort to maintain readiness there. Then when my plans or circumstances dictate, I follow up with an infantry assault that rarely fails. Mind you this only works against a static foe.
It is summer 1942 right now in my current PBEM game (turn 60 something) and I have 27 Art Brigades operating together, en-mass, headquartered by three Airborne Corps attached to a Combined Army which is in turn attached to Vorenezeth Front (The new one that apears at the beginning of June which I use as an Assault Army loaded heavy with Guards Cav and Tank Corps and backed up by a pile of Ind Tank Bn's so that each Corps has 200+ tanks) This Army has been tremendously successful as a launcher of spoiling attacks on German bridgeheads. The Arty is particularily usefull in knocking down German supply levels and thus seems good at restricting MPs to the spearheads attacked, even if the followup ground assaults are thrown back.
I always position Arty behind cities under seige, together with an Infantry Div/Corps for protection.. this aids considerably in the defence, I find, with the Arty showing up as present in almost all combat reports in the neighborhood. I've had the same Arty respond to 4 and 5 seperate attacks around it. Often, during crisis times they are the only units in possition/ready and in reserve status.
Additionally, I have had good success using AT brigades in reserve mode behind the front lines to help Inf against German Panzers, which take hard casualties when faced with an Infantry Corps or two, dug-in and supported by a couple of stacks of AT Brigades behind it. I often create rear-area "road blocks" in strategic crossroads hexes where German Pincers are likely to be encountered during a major effort to pocket my forward lines. Two AT's and an Infantry Division dug in at least to 2 will stop most German Divisions that have had to cut through my main lines first to get there.. against fresh Panzers this option is suicide, so don't try this right on the front line or you get pounced.
As for AA Brigades: I love them too because they also will support defences in neighboring hexes, it seems -they show up on the combat reports. Stacking two AA units together with an air army HQ and then encircling them with air bases provides excellent protection to the bases. Once in a while these AA "forts" (especially 85mm, which there are so many of) can stop a Panzer thrust, if they are at the end of their move and you are (extremely) lucky and dug in solidly in the rear areas with an infantry brigade to help defend/dig.
Thats my two cents on Arty.