There are a few changes that could be made to them to alter how they impact the game.
Slight reduction on their ability to alter terrain. Makes defending key areas slightly easier.
Reduce the projectile speed significantly. Makes them less effective against mobile armies but no change vs buildings
Have the projectile lose damage when it travels beyond the nominal range of the bertha. This will make Berthas built safely at the back of the base less effective and reward riskier more forward building of the unit
Introduce a stockpile and cost to stockpile munitions.
I don't suggest all of these are implemented at the same time, that would be overkill.
I personally like the idea of the unit, but agree that in it's current state it really bag bog a game down as any attempt to push the enemy with ground units can just get hammered into submission by a battery of berthas