I have ALL LED's and no issues. The biggest problem with the LED bulbs is the cheap non-quality manufacturing of them. You get what you pay for sometimes. You stated you bought no-name LED's, maybe it would work a bit better if you bought some error-free CANBUS bulbs instead of generic crap. JUST my opinion.Why would there be a market for LED bulbs if they cant be used in a vehicle.
edit* These are the bulbs I bought and installed Amazon.com: JDM ASTAR Extremely Bright Max 30W Canbus Error Free 7440 7441 Cree LED Bulbs ,Xenon White: Automotive
If you look at them in the pictures you will see they only have 1 contact per side, unlike the ones you were using that have 2 contacts. That is the difference between a 7440 and 7443 bulb. The extra pins are likely what were causing you an issue. If you want to try yours again, bend over the pins on the left to the opposite side of the bulb. You will then have 2 pins on the right hand side of the base on each side of the bulb. Unfortunately most manufacturers consider the 7443 and 7440 interchangeable but t hey do not work this way in this vehicle.
Once again here is an image showing the difference between 7443 and 7440 bulbs.