Here's some things to try.
Hill repeats. Find a hill that takes four or more minutes to climb, preferably one that isn't ball-breakingly steep (tip: don't use Bison hill). I often use this one:
Warm up. Go up it at a steady hard effort. Descend, have a breather, repeat. Start with, say, three or four repeats (tip: don't go too hard on the first one!)
Find a 5-10 mile loop with all left turns and no traffic control. Ride to it to warm up, ride it as hard as you can- aim for a steady, sustainable effort rather than accelerations followed by recovery. Ride easy for a few minutes, repeat. Ride home easy. Time yourself on the loops (this is where you find out whether it's working).
Have a look at stuff on the net about interval training or buy a training manual.
Enter a TT? I didn't think I'd take to it but I do quite a few of them now, mostly club events.
The best tip I ever got on here was to take up Cyclocross. I'm pretty sure it makes me faster, it's definitely fun.
You'll probably make quite a bit of progress just by mixing up your riding a bit. Instead of 60 miles at 16 mph try doing some of those miles a bit faster. Try riding two lots of five miles out at a faster pace towards the end of the ride.