How do I care for a large, neglected plant?
 

I've been given a very large, very old cattleya of some sort. I've cleaned up the old flower spikes and there were some dried up, completely dead psudobulbs that I removed.

The plant is huge. Here it is next to a dendrobium kingianum , and alone.
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Right now it's potted in a clay pot and what I imagine is very old bark mix, with that pot set in a wooden basket. I have the ability to pot it and care for it anyway it needs to thrive. The plant is so grown into itself I'm just not sure how to properly water it without rotting out the interior of the root and psudobulb mass.

I've got a slightly smaller, but very similar mass of brassavola nodosa 'little stars' that I'm planning to mount to a large piece of cedar and suspend it from the ceiling. Until then, it's sitting in a glazed ceramic dish.

It does look to be some type of BLC or similar hybrid. The plant doesn't look to be in all that bad of condition, just needs re potting.
The appearance of the plant, having bloomed out along with the time of year it is now, leads me to think it should have begun new root growth, or will be doing so soon.
As soon as you can detect new root growth I'd re pot it into the next larger size pot, mount or whatever of your choice.

I haven't dealt with potted orchids for many years. Wait for another opinion before listening to me.

EDIT:
When re potting do all the usual things, removing all the old media, all the old dead roots and growths, etc. Strip it down to just the good healthy plants and parts .

Yes, there are probably at least som Brassavol genes involved. The leaves look quite thick and narrow for a pure Cattleya. I second Voyager's suggestion to wait for new root development befpre repotting. You may also decide on division, leaving at least 4 growths per division, but that's up to you.

I could never divide this beast of a plant. I think I'll do best to mount it to a thick slab of cedar so it can continue to grow bigger.

I think in your climate, with the Brassavola heritage, this could also swing on a chain with little or no medium.