I do all my own historic tailoring, and used to run a repro clothing business before I went back to school. If you can sew a haversack, a mechanics cap will not be hard at all.
I have made some of John's clothes and all of mine! Good pattern and a good fitting muslin really help!
I know Simplicity had a pattern that was well regarded, but it's out of print. I believe you can still purchase it on line, though.
I have on cap finished , did a lot of ripping out and starting over. Its not perfect but ok. and have started another,in off white canvas. I think it will be better. Ill post pics,, maybe Ill get the nerve up to try a sack coat. Everything Im sewing is by hand though and I bet that would really take some time.