Did you by chance save the gunk from your water separator? I am thinking if you could determine if it dissolves with heat and nothing was left it would help to reassure you that you had only one clogging material, not two.
Second, did you replace the fuel filter or just warm it up? If the filter itself is passing less than the normal amount it could cause problems. That would be an easy thing to do if you haven't done already. It looks to me on the parts diagram that the bleeder screw would allow fuel to leak out from a line that has a T in it, making some of your previous experiments harder to interpret.
I am clutching at straws here on your behalf because draining the fuel tank could be easier said than done. It is in two halves connected by a large tube with a check valve in it
one of the halves appears to have the oil filler pipe running through the middle
My thought that you could suck out the fuel through the fuel filler pipe won't get the fuel from the left half due to the check valve.
After looking at the parts diagrams and comparing with the diagram from the wsm, there are a lot of discrepancies. The order of the components is not exactly the same. My parts diagram is several years old, so you need to download the one for yours. I am curious about the function, and so as not to hijack your thread, if I get ambitious I will start another.
Edit: I have looked at the kubota online parts diagrams, and there has been no changes since I printed mine, and the 4060hst is identical to the l3560hst.