Over 30 years ago I used my 10-speed for everything and rode it anywhere. I got tired of always repairing flats and installed the solid tubes and they worked like a charm but I haven't had any experience with them lately.
I run Slime in all my bikes now.
After somewhere around 2500 miles, the only puncture the Slime hasn't sealed was from a 3/8" hardened tack like the type used to fasten carpet tack strip to concrete.
The tack entered between the tread and side wall and then got twisted/bent and caused a "V" type cut that the Slime couldn't seal. This was Slime designed for bicycles, the Slime designed for autos or ATVs might have sealed it up.
You could try tire liners but they can be problematic and if not correctly installed can cause more flats.
You can make liners out of old tires and/or old tubes... similar concept to thorn proof tubes... they're thicker
Any solution will most likely add some weight