barely staving off invasion.
Whatever you do in Civ4, never ever spend time worrying about an AI invasion. The AI is utterly worthless at those and won't pose a threat. If they ever send some silly units, you can laugh at them a bit before killing them and going on with your own business.
Looked at your game and it seems you've fallen into the traditional cuirs/cannons trap. Don't combine those. If you go for cuirs, forget about Steel and tech straight to Rifling for Cav upgrades. If you go for cannons, forget about MT and tech straight to Rifling to draft Redcoats. Now you have an army of fast mounted units that apparently is moving very slowly. You got MT over 70 turns ago but the first AI isn't dead yet. 70 turns should be enough to cap the entire world.
For faster warfare, you just have to keep constantly moving. That stack of cannons in Akhetaten should certainly not be healing. They should be heading straight towards the next target. Wounded cannons are just as effective for bombardment and there are plenty of healthy cannons to deal collateral damage. Cuirs could heal a turn or two and still catch up with the cannons. Though in this particular situation I would rather move out immediately with the stack of cuirs (including the wounded ones) and forget about the cannons. The cuirs and cavs you have down south should be enough to finish Rammy in 2 turns. (Yup,
dead t257, no problem.) Overall, heal less and move more aggressively. And don't leave strong units behind defending conquered cities! Having cuirs and cannons stand around as military police is a massive waste.
You don't seem to be whipping much at all. Instead you have lots of workshops that gain +1
from Caste. Caste would be the stronger option here.
And yeah, lumbermills suck bigtime. Having unchopped forests around your capital this late is a crime.