I don't think anyone makes OD dye, but you can.
Here's the proportions for RIT liquid clothing dye: OLIVE DRAB..............1/2 cup Dark Green......1/4 cup Dark Brown.
I think they also sell Dylon dye in the UK. This comes in Olive which is close to olive drab, but is a bit bright. Perhaps three parts olive to two parts brown would get you close to an Olive Drab colour.
As for the polyester stitching issue, there's nothing you can do about that but live with it. I kind of like the look - it's rustic.