I think I heard something about Singing Frogs using burlap rolls to germinate carrots during summer and they have excellent results with it. I'm planning on giving it a shot next year, never thought of it as a possible landscape fabric though, might be possible, just not sure about how quickly it'll break down. Anyway I was planning on purchasing it from Uline, their prices are cheaper than what you found, they specifically have some listed for AG, and they have a wide range of widths.
I've used burlap as shade cloth for lettuce years ago. Works great just doesn't weather very well.
When I did a workshop at Singing Frogs Farm they used burlap on direct seeded carrots to keep the soil cooler and moister for longer.
A friend of mine (at Tiny Farm Blog) has written a few times about using burlap: https://tinyfarmblog.com/tag/burlap/?cn-reloaded=1
I've always used coffee sacks for carrot germination -- some are even 30" wide to fit my beds. The double layer can retain moisture for several days, which helps if you don't live on site and/or have multiple locations. If there is a coffee roasting facility near you they may give them away for free. I try to soak them overnight in a big tub first because top down soaking with the sprayer takes 12 years. Also, gets the most soluble ink out of the material.