I just bring a hoe with me the first time I take a cart somewhere. Using the "Level" function, you can carve out a rough path with ease. Chop down whatever brush/trees are in your way, and pick a route that's somewhat level. If there aren't any routes, you might need to do a bit of picking, but it's not too bad. I generally go 2x the width of the "Level" for the hoe. Gives you a little bit of room to manuever.

You don't need smooth roads, just something that reduces the slope in places, and gives you a reasonable path to follow. Ruts and small holes aren't going to slow you down, and you should always have 10 wood to build a quick Workbench for field repairs.

I keep my weight around 1000-1400 at most, and my inventory empty except my usual gear. If your cart breaks, oh well, you have your 10 wood for a Workbench, so just grab the mats it dropped and build a new one. Eikthyr is absolutely fantastic for this btw, the reduced stamina cost for running is a godsend when you're dragging it back home.

This works really well for silver mining as well. I break my cart down, stick it in my inventory (or stash it in my boat), then head up the mountain. Quick Workbench, cart, and fill that sucker up. Then, just kick it down the mountain. Once it hits the bottom, load up your boat, break down the cart again, and off you go. I usually clear trees and rocks where I'm going to boot it down, just so it doesn't get stuck too much.