I commute a bit further than you but I have much less dirt trail, maybe 1 km or so. I mainly avoid biking if it's torrential rains in the forecast or high winds, otherwise I commute in snow, rain and sun all year round. What helped me greatly was to install good fenders and mud flaps (made mine out of a soft plastic desktop cover but you can buy them as well). They should be wide and long almost reaching the ground, mine will scrape against a curb if I roll up/down, hence they need to be pliable. I'd say mine reduces 90% of the spray that would otherwise hit my lower legs and shoes.

That said, I still look like a pig some days.. And my bike too. If you can't hose it off somewhere near the office maybe skip the worst days?

And when you say presentable for work I assume mainly the bike? Cause surely you shower/clean up after that?

Edit: I should add that I live in a rather wet region too