More training all round sounds like the ticket to me. I wouldn't worry about doing specific "speed" sessions yet although it may be very beneficial to train in a group. They are the top half of the cake - if you are worried still about weight then basically more running all round will make a real difference. If you can't keep up off road then practice!! Run off road more if you can.
Doing more formal sessions can be very difficult if you don't have the training foundation to back it up so make sure you follow the sensible advice above and don't overdo it too early and you should be able to improve nicely.

Finally, best of luck.