I dunno, maybe this is just me... but I think wearing your uniform to get free upgrades is not only professionally unethical, but also may cause a misperception among the civilians that see you in 1st class in uniform. They may think it's their tax dollars at waste that went to the purchase of a 1st class ticket for you. Remember, it's not what's TRUE but what may be PERCEIVED to be true.
I've travelled in uniform before, and also have been offered the upgrade on 2 occassions... I accepted the 1st time (and subsequently thought more deeply about the ramifications of accepting such a gesture). On the 2nd, I graciously declined and expressed my gratitude for the thought...
Well I only did it the one time and graciously accepted since I had a 300lb woman spilling onto me, and I could practically smell the chicken bones in her fat folds. I don't think anyone noticed or cared, but who knows. I think you're worrying too much about it. If I travel in civvies and use my mil ID, I would have NO issues moving to first class, but the opportunity hasn't presented itself yet.
Airlines have been supportive of the military pax in my VERY recent experience, and I think people are supportive of it. Military folks were allowed to board first before general boarding on my last flight, which was nice, and all the other pax looked pretty happy about it.