Comintern is my favorite doctrine to play and I use the SP units extensively. In the hands of an active player, the SP arty and SPRA can be used very effectively to bombard and retreat. You can essentially completely destroy units without taking any damage in return. I once took out a 42 unit doomstack from an active player without taking any damage whatsoever. You just bombard them and if they're giving chase, move in half hour increments so you can bombard again before moving. You have to be very active for this strategy to be effective; it's not for the casual player.
I never upgrade my initial arty and rocket arty except maybe as a luxury very late game. Instead I send them into the mountains as they get a bonus from mountains and the SP version doesn't. Although with Comintern, you are always better producing new instead of upgrading to fully utilize the doctrine reduced production advantage. Although, I'm guilty of upgrading some units as I don't like having obsolete units around. Try spamming low level then upgrading by skipping a level. This is best done with cruisers and infantry, but could be used for others as well. Even better if you can upgrade just before you finish researching the level 3 and you only pay to upgrade to level 2, but it will increase to 3 anyway.
Countering air power will always be Comintern's Achillies heel. You'll just need to read the map. Check the newspapers often to check what other players are using. If you see reports of units being destroyed by bomber wings, make building interceptors a priority along with upgrading your AA. Sometimes on the 22 player map no one uses air power and you don't need to worry about it, but don't just assume that! You can also check the profiles of other players to see their progress towards achievements using air units to gauge how likely they are to use bombers or recruit spies.
You're best expanding in phases. Days 3-5 are best once you have enough rocket artillery built, then start researching both SP arty and SPRA on day four, and start building them on day five. Also on day four, focus on getting your secret lab and ordinance foundry upgraded as high as you can get it so you can start rolling units off the production lines as rapidly as possible. You'll have enough mobile artillery by day seven to start attacking with them if you can identify targets weak in air power, or you can wait until days eight when you have sufficient SPAA built. You can always build aircraft carriers just to use with interceptors along coastal areas. Another strategy is to hold them in reserve until you deal with their air power. A good strategy is to send a stack of infantry supported by your arty, RA, AT, and AA into your opponent's hills. AA receive a terrain bonus in hills and the infantry add to the damage bombers will take. Plus if your obsolete units get worn down a little, it's not a bad use for them if you can neutralize their air power. When they attack you and you've weakened their bombers enough, unleash your SP stacks.
You'll also need to protect your SP units on the ground. I like pairing armored cars and tank destroyers to maximize your ability to retreat if an active player is trying to engage you in melee combat. Don't stack these units with low mobility units like anti-tank or regular AA or you're squandering their potential. Just use TDs and ACs to keep up with and protect your mobile artillery, bombard and force your opponents to either be bombarded away or attack your defensive units protecting your mobile artillery. If you have to do any amphibious landings, cruisers are your friends to defend against attacking bombers, or at least the ones on patrol.
Hope this helps.
