The HE-500 can be a good alternative, but it depends a bit on your mod configuration and the other equipment in your chain. It definitely was the headphone that ended my basshead can search. With the fuzzor mod, a decent cable and the right pads it's not terribly far off from the LCD-XC, to my ears.
What you heard about the HE400 isn't quite right. It has bigger bass, yes. But it's NOT sloppy or muddy at all. It's very, very clean, tight and fast bass. The problem with that one is the other frequency ranges. The mids are quite colored (which can be a good or bad thing, depending on your point of view) and there is a pretty significant spike in the treble. It's a good headphone, one that I've held onto, despite many other significant upgrades... mostly because the bass is so great.
The HE560 is just very neutral and very linear all around. I wouldn't say it sounds the same as the T1, but I can't see owning both for any reason. They check a lot of the same boxes.
I believe the new 400S model is a bit more on the neutral side. I haven't heard the 400i.