So, here's what I did and it made a profound difference.
First, I never wanted it to sound like a telecaster, but it was pretty muddy. With the existing pickup rings (these were 3/8" at the neck and even deeper at the bridge, I could only get a certain amount of distance from the strings (adjusting pickup height) without having to raise the action. I didn't want to do that. I like the action where it is.
So, I bought pickup rings for a Les Paul (1/8" at the neck and 3/8" at the bridge,) installed them, and moved the pickups. It made a great deal of difference. The tone is brighter, more articulate, and even when I crank it up or use an overdrive, it doesn't get muddy anymore. Current strings are 9-42 boomers - I prefer 10-46 and may switch to that later. The 42 set was what I had at the workbench.