[Disclaimer: I am currently getting rolled by a wall of heavy artillery in one of my games. It struck me as a topic with discussing, as I am doomed.]

Anyway, with limited flanking room and limited income, does anyone have any favorite strategies for cracking 3-deep artillery walls? My cannon fodder approach seems to be only slightly delaying the inevitable.

I've been beaten up in a similar fashion - 5 hvy artilleries with a constant spply of cannon fodder blocking my units from getting at them, every turn the artillery slaughters everything I have that's trying to push through (even when I was managing to spit out 2 heavy tanks every 3 turns)

I've gone through by applying a false blitz attack strategy, but you can not allow the player to build a 3 deep artillery wall. Once that happens your pretty much screwed. Build two attacking units, and place them within each others ZOC limits. You have to encourage the arts to fire on the group that looks like the attacking group. Its best use with raiders and troopers. The secondary group that plans to break through needs to start with raiders at their farthest movement range. Attack with those first at one wall point and leap frog the rest of the group in. The best place to attack is a unit that has two or more exposed hex faces. Also, live with the fact that you'll lose all your units. The goal is not to destroy the H.Arts but to knock their health to 6hp. At 6hp H.Arts are not as effective against tanks or H.Tanks. Your opponent will need to spend about 2-3 turns on repairing and not returning fire. Or they will retreat. Also, always get an ART sitting on a base to fire. It prevents the opp from building.

My initial advice is to make sure your opponent never gets a wall of artillery on you. I've went to great sacrifices to destroy artillery before they begin to mass up, and I don't mean wound...destroy. One thing for certain I will say is that, most of the time, it is pointless to simply damage an artillery, as they can just pull back behind their lines and 6 to 7 turns later...you have a fresh artillery on you.

Another way to avoid heavy artillery walls is also to continuously kill the fodder...once you let your opponent get a comfortable cushion of fodder, artilleries is all he will build. That means staying on the offensive with raiders and tanks. Keep your raiders in squads of 3 to 5. With the multi-attack bonus rule, raiders can be very powerful if there are enough of them.

If you opponent does get a wall of artillery, then the only way to break through is with one huge offensive. Retreat and save your man power...force your opponent to advance. Make him distance himself from his source of reinforcements, while you get closer to your source of reinforcements. When the time is right throw an all out attack on him. Have some artilleries of your own to soften his fodder wall and some Heavy Tanks to absorb alot of his firepower.  Give him too many targets to  attack, so that he will either have to hold his ground and lose his artilleries or retreat. If he retreats you have him, since those heavy artilleries move so slow, and his rearguard is already weakened from your initial assault. If you can't force this choice on an opponent in the first couple of turns, you are not ready to attack him continue to pull back out of range.

The problem comes when you don't have room to manoeuvre, either because the map is small or because moving back will mean you lose bases

Aye. 3 deep is too late. When you're there, the only hope is to send in your own HA in artillery dogfight.

Say if you're facing a front with 5 HA against you, one way is to move your own 5 HA all in one turn 4 hexes away from his own HA. Either he shoots or you shoot, but it'll bloody. Back on your turn, you retreat your own wounded art and move in new ones. I know, you're like, what, that's a lot of artillery. But yes, a solid (screened by units) wall of artillery can only be busted by getting at his art. I know it's like, well, I don't have 5 artillery in my backpocket. But if your enemy have them in you don't well you're done for.

Finally try to follow what your neighbors are doing. If they build 1 HA, I try to build one... Arm race thing. Otherwise after many turns he's now having 8 art and you're having 3... Not good. 

Back up and build your own artillery.  With a couple heavy artillery of your own, you can back pretty far off a base and still have it covered.  Try to drag opposing heavy artillery into weak positions, like bases, forests, or set up a 2x1 with a mountain blocking a spot in his artillery line.  If you do get a 2x1 on the end of a line, shoot from the outside in: if your weakest unit is on the end of the line, and you kill the end of his line, you're free to repair.  If you're low on cash, substitute raiders for heavy artillery in your line.