my first advice would have actually been to maintain your boxing training while lifting weights.
The best thing you can do at this stage is to shadow box, and half the time add 2 lb Db and realy concentrate on punching fast.
Speedballs ( floor to ceiling ) are great espiecally if they are tightly sprung. Use one of these and work on doubling up your jab. By this I mean hit it twice before it springs towards you. As you increase your speed tighten up the ball, this will force you to be quicker.
Another problem if you always lift heavy ,will be muscular endurance. You will probably start off relatively fast yet in 45 - 60 seconds your arms will be dead tired. to improve this you will have to put youself through 2 - 3 minute rounds of bagwork at a time.
It's just like building fitness. When you do punch try and remain as relaxed as possible untill actual impact, this will help a little.