Are you sure you have a drain? Does the battery actually die if you let it sit? Or does it act the same way day after day?
Did you get the drain fixed, or are you still trying to track it down too?
Hate to say throw some more money at it, but it could actually be a second defective starter relay. I know you just put a new one in, but I've had them bad right out of the box before. And so have others here.
Is the starter relay/solenoid bolted to a clean, rust-free surface too? The relay itself needs a pretty good connection to the body through the bolts. If the holes are super rusty or loose, it might act like this too.
If the starter is offering too much resistance, it might act up similarly. But you're saying you tested the starter and it's working ok?
What about the engine (inline 6 or V6?) itself? Does it turn over easily by hand or with the starter when you bypass the relay?
How did you test the starter before? On or off the vehicle?
You said you checked the grounds, but what about the positives? How old are your starter cables? How large? I've had the short one from the battery to the relay fail on me before, even though it wasn't that old and looked perfectly good. Just wouldn't pass enough current through it to make things work.
If they're old or have had some corrosion on them in the past, or ikf they're questionable but you figured they'd work for now, might consider new ones.
When it comes to battery cables, when in doubt, replace them. Just cheap insurance.
And even though this is low on the list of possibilities, it's still a thought. What about the ignition switch? Have you tried jumping the starter relay between the battery and the small terminal with the Red w/blue wire on it? Does it still just hum?
What about jumping straight from the battery side of the relay to the starter side? Is this the test you did before?
Just a few things to think about.
Hope you get it solved. For such a simple system, they sure do seem to have lots of potential for trouble!
Paul