I would consider intervals that last minutes more 'tempo' training; I think you would get this from your group rides considering the pace they are riding.
Technique is too complicated for this forum, but in my opinion sitting in is not a great way to make friends and not a great way to train/improve. Riding in a group is all about moderating your effort but if the others are so much better than you that you have to sit in just to keep up then it will not help you improve.
Showing your face at the front is always a good idea but the technique of 'through and off' is difficult to master. Ask for help because many people go through too hard and create a gap between themselves and the rider behind this just disrupts the rhythm. If necessary miss a few turns at the back and then do some more. In my opinion it is better to do this and get dropped than to simply sit in if you want to improve. Again let the others know what you are planning and ask advice
Riding 60 miles at 18 19 mph is not bad! I am assuming that their pace varies and the road is not pan flat. There is a lot of technique involved here, ask one of the other riders what they think of your style, are you pedalling too fast or more likely slow.
I would be surprised if they do not help, but the advice may be contradictory
Work on speed, tempo and stamina;
Speed = short intervals 40 seconds hard 20 seconds rest (40 20's)
Tempo = your club rides
Stamina = get the miles in.
130 miles a week is likely to yield good results.... give it time