It's a Baja isn't it?
"I think the issue with the tele is that is sounds relatively weedy and doesn't give me the natural drive I would like..."
That's exactly how I felt about my Baja for the first 3-4 months.
It's not you, some people love the stock tone/behaviour, some people don't. I didn't, it was ok on a "Andrew's playing very well day", but on an average day it was very disheartening. I had the luxury of picking up a different guitar that suited my mood. But it meant I rarely played the thing.
But I fixed it...
First thing (cheap), lift the control panel and look for the treble bleed capacitor across the volume pot. Get rid of it!!
Treble bleed cap = don't lose top when you roll down = weedy tone
Second thing (cheap), fiddle with pickup heights a lot. Nearer the strings = thicker tone. Note, however, this didn't do it for me with the Baja pups (even when I tried them in another tele). I improved it, but not enough.
Third thing - get a set of Blackguard Flat 50s. The basic yummy-baja that you do like is still there, but it's thicker, more responsive and all round yeah...