04.5-06 is the problem child LLY. They are good engines overall, but the cooling system is inadequate. In 06.5 the LLY was mechanically identical to the LBZ, but had less power entirely due to the tuning. You can tell the difference between the two as the early LLY has a 5 speed transmission and the late LLY has a 6 speed transmission. You can fix the early LLY cooling system by swapping out the original cooling system with an entire LBZ cooling system (including the pump and thermostat housings, fan, rad, larger hoses etc) and it will no longer overheat. The early LLY also has injector issues, but they are not as prevalent as in the earlier LB7 trucks. I'm running an early LLY in my caddy and while it needs injectors, it serves me well. You could get a ZF-6 behind the late LLY, but not the LBZ. You can take the tune from a late LLY and update the engine tune to make a proper manual trans LBZ as they both use the same PCM.
The Allison is one of the best automatic transmissions available on the market. They are beefy and hold up extremely well when run in a stock application. You'll find the limits of them pretty quick when you are putting out a lot of power though. Limping the transmission is caused by slipping the bands. A limped transmission is a damaged transmission and it will limp under less load in the future after it has happened once. 5 or 6 speed alike, you'll be very happy with one. The ZF6 is a smooth shifting and fun to drive transmission, but you will need to spend a good lump of cash on a solid flywheel and dual disk clutch assembly to hold up to more than a very mild tune. The ZF6 also has a bad habit of breaking input shafts as well. I find that low speed driving suffers with the ZF6 as the engine tends to get into a harmonic with the transmission which cases it to rev up / down rapidly and the whole vehicle to shudder. They also have a lot of gear chatter without a dual mass flywheel and are quite noisy in general. The ZF6 is also a rare transmission and finding replacement parts isn't easy when you do break them. I love em and run one in my caddy, but they are not the end all / be all of transmission options. The Allison is a much smoother transmission to run and they are always in the right gear.