To counter tanks, I barely ever used MAXes anyway. Drop 11 engis on a nearby mountain with AV turrets and nuke them one by one. If they are not even moving, you might as well drop with C4 and pizza.
Every way to counter air pulls troops away from your main defense/attack force, meaning there is no effective counter to air at all - they always reach their goal of decimating the number of active ground forces. A tank column can be destroyed, but a huge air zerg can just take cover and act like a never ending conveyor belt of doom. The only way to get rid of them, is to nuke the known high end farmers with lockons or single use counter ESFs (so they go farm easier targets somewhere else) and hope for the other to disperse.
Regarding your entrenched base... How entrenched are we talking about? I've barely ever seen my guys rolling with a MAX crush, unless the enemy had a significant number of MAXes themselves or time was really really short on a defense (<25s left until hostile cap). If it's a single room/building, work your way through there with EMPs and Concs. If it's a whole base, drop on high grounds and cleanse it top to bottom. Preferably from at least two positions and, if needs be, air support for cooling your LZ... Or artillery, in case AA is present and the geography allows for it. Those squads can then split between some who cut off support routes and some who entrench themselves on the point. If you have the numbers, you can also designate people for bringing in Sundies, additional spawn galaxies, indoor Harassers and so on...
And if you really can't get inside, because the enemy has sooo many players at his disposal, leave a token force along the lattice to slow them down and leapfrog back to entrench yourself in their own base after they moved out. Should you then be overrun because you're outnumbered higher than 1 to 6 or something... Fight somewhere else. Stop the enemy at a lattice node or a different base where you have the advantage. Demoralize them by repeatedly farming them and organizing counter attacks with allies. Disperse the zerg by hunting their spawns and get rid of the highly organized platoons by attacking a different lane, where they don't have the numerical advantage.