These fingerboards are a resin coated wood, so a re-planing may not work very well. Try adjusting the truss rod. Go slowly, a quarter turn at a time. Tune up and check for the buzzing after each quarter turn. I had to fiddle with mine when I first got it. It takes a while, but you only have to do it once.
I also had to change the strings. The stock strings are terrible. I use Evah Pirazzi E and A and weedwhacker D and G. I play a full set of guts on my double bass, and I think set-up gives me a feel and sound that is close to gut, but it's cheaper and does not require maintenance.
After I got my Stagg back from my guitar-tech, I have lowered the bridge, with it being slightly higher on the E side. I also adjusted the truss-rod several times, and have the action down as low as I can get it, without too much buzz in the first-fret area. I'm still working on it, and in talking to my tech, he had noticed a slight hump in the 3rd-4th fret area, and have been meaning to have him look at, and try to straighten the neck so I can get a lower action. I'll let him know about the resin coating, and see how much work, and dollars, it would take to make it more true.
But at this point, it plays well enough as a learning instrument, so if it's a couple hundred $$ to make it better, I'll do it. If it's a lot more, then I'll just start saving up to buy a better built instrument. With that in mind, the Eminence bass I saw on Bob Goliher's website looks promising, and is offered in a left hand model. In case you're interested it's here - [Invalid or Expired Link Removed] - although it ain't cheap! (@ $3200)
My problem is finding ANY basses built for let handers.... But the Stagg will be just fine for now....

