I just moved away from Gravel King SS 43mm tires after 3+ years of use. They have been incredibly reliable and roll fast for the surface type and mix that I ride.
...but they were an infuriating experience to mount each time I had to do it. Luckily that's like 0.0000003 of my life. But yeah, it's infuriating.
Why don't you start riding some gravel now and see how you like the tires you have? Then change tread/width/quality if you don't like something about your current setup.
Seems better to go into a purchase with actual feedback.
As for general comments...
- your tire width is very common for gravel riding. If you go wider, sure a 43-45 may help with comfort.
- tire construction, quality, and weight are very real. A 40mm tire can feel like hell and it isn't the width, it'd the thick sidewalls and hard cading. Meanwhile, that width may be great and you just need a better quality tire in that width.
- the Byway is a very general all around mixed surface tire. Not much tread and that's fine for most gravel riding where width is more important than tread. Something high quality and fast rolling will probably be better than heavy and significantly treaded, based on your description. Guessing though.