i just looked up a Fuji Absolute 2.3 and see that it appears to be a flat bar hybrid or trekking style bike. Since it sounds that you already know the importance of working on fitness and riding more miles, I’ll offer a few equipment suggestions.

1) Can you try your same route on a decent road bike? Before you commit to buying one you could borrow one, buy a used one in your size for cheap or ask a good bike shop to let you test ride one for your regular route?

2) Clipless pedal/cleated cycling shoe usage. If you are not using “clipless” pedals I strongly recommend that you get a set ASAP. In my experience, you will achieve an immediate efficiency improvement of 10% or more on your very first ride. So, just out of the clear blue (if you are riding with “gym” shoes on flat pedals) you could immediately see your average speed go from 11 mph to 12.1 mph just from clicking in. The magic here is that the rigid soles on good cycling shoes greatly aid in power transmission on the down stroke and the fact that you are clipped in recruits opposing leg muscles (hamstrings as opposed to quadriceps) on the upstroke of the pedal circle.

3) Just curious about your 700X35 tires. If they are standard issue hybrid tires, they are probably quite heavy and maybe not even rated to be inflated much above 75psi. For not much money you could swap these out for faster tires in more of a 700x32 or 700x28 size. Now that Continental has released the Grand Prix 5000 tires, some of the mailorder places have been running crazy sales on the well regarded Grand Prix 4000s ll tires. I recently got a pair for in 700x28 for under $60. If you want to get even better performance from the tires you could run them with Vittoria latex inner tubes. There is a bit of a learning curve to successfully mount them without puncturing the first time but once you get it right, these make a noticeable improvement on rolling resistance and grip. My experience with the latex tubes is that they do not flat any more often than butyl tubes once installed correctly. They do lose air daily (~10-20 psi per day) but topping them up pre-ride is a good habit to get into anyway.

4) As you get stronger and reduce weight you might look at your gearing and see if you can tweak it up a few notches. With your 48/38/28 crank you’ve already got the capability to have quite a low climbing gear while in the 28 tooth chainring. So the 34 tooth cog in the rear might not be necessary. If it is a 10 speed cassette, why not get a 12-27, 12-25 or my favorite with triples a 12-23 ! Any of these options could be sleeper fast because your jumps between gears are smaller which will allow you to optimize yourself to your faster buddies and keep you in the zone. Climbing the steeper climbs is going to be a bit harder so you will have to practice your most epic local climb a lot. See what works for you. Are you more efficient as a seated climber? I know it is not realistic to stay standing for long intervals on longer climbs but I do find that alternating short sections of standing on the steepest parts can be of benefit. And then there is that old technique of climbing of shifting into a harder gear just before the summit of the climb to rest your legs momentarily as you crest the summit and jump start your descent. At your height and weight you could potentially be fearsome as a descender. Here is where having an 11 or 12 tooth cog on your cassette comes in. Spin yourself up to your max speed, get in a tuck (drop handlebars help here) and go for it! You may crash, but most people do at some point and when you do your adrenaline will be pumping for sure!

I have been as heavy as #265 and I’m a hair under 6’ tall. Currently I’m at 195# just for reference. I’m also 56 years old by the way.

I hope my suggestions are well received. They are things that have worked for me. I notice on these forums that folks get preachy and dogmatic in trying to help others. Ultimately you know your trajectory. You are right to inquire on the factors playing into gaining more speed. It sounds as if you are already going to blow by the avg speed plateau. These things tend to be moving targets anyway.