As a 60+ yo myself, consider age being a factor. We can try to outrun it (outride it actually), but it will creep in an have an affect. But I don't believe this is the primary cause - just something to factor in.
It could be the seat that you are using is causing the issue you are experiencing. Wide and soft/squishy seats are usually not the best for riding longer distances. They may appear to be by visual perception and physical touch, but that is deceiving. For relatively short rides/utility cyclists the soft/squishy seat may serve a rider well enough, but for most riders, a firmer (but not rock-hard) seat provides support in the right places, and the correct width and shape for YOU supports you on your two sit bones.
I would recommend looking at your seat selection first. A local bike shop may be able to fit you better. The shop may also have test saddles to try out. Try different models/shapes in the real world on your bike. You might be surprised at the comfort you discover and may resolve the pain in the glutes issue you are experiencing at the same time.
Your use of good bike shorts/bibs with a padded chamois is a smart one. Differences between the quality/density of the chamois is not as stark as the differences in saddle shape/width/firmness, but it can play a part. Work on the saddle choice first before changing around different bike shorts.
Beyond the seat selection, your pain could be compounded by your fit to your bike. A competent bike fitter can identify problem areas with how your bike is adjusted to fit you that could be the source of your pain. A good fitter will accommodate for age, gender, the riding style, and even for injury or skeletal limitations. A local bike shop or a community cycling club/team, or other experienced riders would be good sources to locate a good bike fitter, and if your pain persists, I would suggest seeking out their professional advice (you are the engine and it needs to be aligned correctly to the machinery to operate efficiently, without pain, and avoiding repetitive motion injury.)