Before there were "Gravel Bikes", we road skinny forked bikes on trails and less technical single track. Your bikes will be fine. One of my road bikes uses medium reach brakes, can fit 35mm tires with room to spare, and I raced Cyclocross on it. No Problems. BUT, I am not discouraging buying another bike
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I don't do: disks, tubeless, e-shifting, or bead head nymphs.