Rushbarb,
Run your "safety test" several more times to be sure. Another test I would do0 is this. Put on the safety, then pull hard on the trigger. Then release the safety. If the gun fires you have an unsafe condition. A thorough cleaning with brake pad cleaner or carb cleaner of the the trigger safety area will usually solve the problem.
After taking the barrel action out of the stock, point the barrel over your shoulder. This will give you a front view of the trigger. The top screw is to adjust over travel. The bottom screw adjusts weight of pull (this is the one you adjusted). The screw behing the trigger adjusts sear engagement. Don't mess with this one unless absolutely necessary.
You can find this whole adjustment procedure up on "Sniper Country". I strongly suggest that you visit them.