You don't need a better bike, just better wheels. Personally I find 26-27c tires to be a fine width, I'm currently running 25 on my road, 25 on my track bike and 27 on my cross bike for summer use, and I find the tires to be fine and wouldn't like bigger than 27 unless I was riding dirt or gravel. Wheels absolutely need to be 32h or 36h, my gravel touring runs 32h rims and I'm typically within 12-15lbs of your current weight and another 40lbs with load so with the right spokes it'll do fine with 32. Spokes should be 13 gauge at the hubs, most spoke companies make that, built with a decent weight mtb rim and a decent hub. I used wtb rims that have no problem with 25c tires and can go out to 38c with no trouble but work well with a road bike. You want to find a shop that can build something similar and can do it for about 400.