Get some narrow cross tires with less tread on them. You can't put a road tire on and expect it to perform as well as a cross tire.
I ride my cross bike 2-3x a week on a mix of road/gravel/dirt/singletrack. I usually ride Kenda Smallblock 8s in 32c size. They roll well enough on pavement, but give good grip on the dirt. And since they are 32c, they allow me to run less pressure than you could ever run on a road tire, regardless of what it was...
I run 50-60 pounds and they are just fine.
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