OP again,
Well, I purchased a Shimano Ultegra 6800 wheelset and added Conti GS 4000 tires. I rode a 58 mile loop with a variety of terrain with my younger faster friend. Did I get dropped? Yes. Did the wheelset / tires change make a difference? Yes.
First, my average speed was a personal best for a long ride by 1/2 mph. I noticed it was easier to accelerate on minor climbs and flats. While there was no apparent difference to me on three 5-10 minute climbs where I got dropped like I always do, I did not get dropped on any of the shorter hills and climbs.
So, I would have to conclude that if I do not want to get dropped, I need to start interval training as suggested.
I am glad I got the new equipment; it did make a difference.