All of the above advice. But occasionally throw in an exercise where you mix up eighths and sixteenths, say L_L_L_L_/LLL_LLL_ or L_L_L_L_/L_L_LLL_ (and with the right, of course). This way, you're not taxing your hands so much but can work at a slightly faster tempo. As your left hand gets better, you should work on balancing your hands as well- Still eighths and sixteenths but maybe: L_L_L_L_/LRLRLRLR/L_L_L_L_/LRLRLRLR. And as simianhacker says, "Play to your slowest hand". Agreed. Though I would qualify that to say "...but at the volume of your strongest hand." Bring your left hand up to meet the level of your right, don't drop your right down to meet your left, within reason. So as you're trying to build up, work on medium to loud strokes with a full range of motion. But also work on playing quietly.
Try different surfaces as well: hard & soft pad, snare, floor tom, pillow, moon-gel pad, etc. The object of the softer surfaces like a pillow isn't to muscle things out by slamming the sticks down, but to lift the stick up after each stroke. You'll build stamina and feel each stroke. The object of the bouncier surfaces is to control the stick- not over control it; you're letting the stick do the work. But you're also not throwing the stroke away.
Cleanliness and control is the goal, but you may experience dirt and slight tension, at least temporarily, when you increase tempo. If it's more than a moment, take a break and go back to it. If it keeps happening, drop the tempo back down a bit. You don't have to go in 5 or 10 BPM increments either. One day that may work and another day it may be a challenge to go 1 or 2 BPM faster. And concentrated practice is the key. 10 minute sessions with purpose; where you're practicing at your limit or trying to push past it will get you much further than an hour of playing in your comfort zone.
Anyway, this is my opinion. Although I reserve the right to edit it after reviewing in the sanitized light of day, tomorrow.