1. Lose the weight. That's by far the biggest thing as you already know.
2. Get "The first twenty minutes" which is a really well written book that goes into some depth on High Intensity Interval Training which is probably your best fundamental approach to gaining speed.
3. Consult your doc and determine if you have low testosterone and whether you want to approach that option. I have low testosterone but am not going to take anything for it. There are potential downsides and for me there is no point in it.
4. Look at an overall weight training program or exercise program that addresses core muscles and such. Being able to properly rotate your pelvis into position and get fully on the drops for extended periods without discomfort will get you another 1 to 1.5mph all by itself but maintaining that proper pelvis positioning is a learned thing and it took me two years of riding just to be able to begin that.
5. Be 100% confident your bike fit isn't just good...it's excellent. Proper stem/reach is so critical and the old plumb drop from the knee may not really be the perfect thing.
6. If you are on the drops easily and comfortably, or if you are moving toward that, consider trying a Specialized Evo Romin saddle or one of the Romin type saddles with a bit of a curve to the back side that is best suited to being on the drops.

It's easy to say that we should be happy to do 15mph and while that's true, for many of us including myself, it's a matter of challenging ourselves to do as well as we can. There will always be somebody faster and somebody slower. My goal is to not judge myself against anyone else because that's an automatically endless quest with no win in sight, but I do enjoy trying to understand and work toward the best level of fitness and speed I can do.
One odd thing I finally bought that may not make much difference is a pair of very light shoes. I used spd mtn bike shoes for a long time and now that I have lightweight road shoes my old shoes feel like I'm lifting a brick when I put them on.
But all of this pales in comparison to that weight loss....I'm a clyde but I'm still working my way downward. I'm 61yrs, 223lb but down from 285. I can roll for a good period at 17mph on the flats with no wind but I can't keep that up forever. I can do a pretty steady 16 for a long time and of course even that is a huge improvement for me compared to last year and the year before.
Sadly each year brings with it some further diminishment in our strength and speed and I don't know how that all balances out with our efforts at this point in our lives but as long as I have more weight to lose I think I can continue to improve my speed and fitness just on that approach.
Enjoy the journey!