You might want to "audition" a light sage green on the panel and camo--it seems to really disappear into lots of fabrics, especially the camo. Maybe outline the deer and some of the features on the panel, then use the sage green to SID around the orange, then just a meander on the camo--bet you'd hardly see that sage green.

Light sage, beige, light gray - all seem to generally disappear into many fabrics. I personally love variegated threads and use them all the time. And I agree with marking the fabric somehow. There are chalk markers that pretty much dust off. The water erase markers are also good, but it can take a lot of water to remove them. They can become permanent if ironed or washed with detergent. Good luck!