I’m sure on a lot of earlier Vulfpeck videos he’s playing through a Roland Bass Cube.
Doesn’t explain huge amounts - but noteworthy as that has a setting called bass360 which sonically seems to fit the bill - and a one size fits all button compression.
In saying all of this, Ive just done a set of demos with my CS Jazz, an 80’s Yamaha BB and an 00’s Yamaha BB. All sounds like me.
He has a very particular attack...on faster passages it’s almost as if he wanted to sound like Jaco so much he missed Pastorious and found his own sound via Rocco Prestia.