Major, The 3" strop is tougher to break in than the old standard of 2 1/2" but some grunt work will help to soften the leather.
I have been looking around the house to find a good household "tool" to recomend for use in breaking the fibers in your leather strop. The best I can come up with at my house is a metal folding chair, The framework is constructed from 7/8" round metal tubing. I think the top of the backrest would work to soften up the excessive stiffness that is problematic for you.
A chinup bar that goes across a doorway, or maybe a round table leg might work well too, even the top rail of a chainlink fence might be considered.
Just very tightly pull the leather over the rounded surface causing it to stretch.
I would start with the rougher side against the round surface for a few hundred passes before turning it over.
When putting the top grain down I would first hang a piece of fabric over the tool of choice so that it will slide with the leather so the stropping surface will not be abraided by the tools surface imperfections.
Just for fun I just measured the thickness of 5 leather strops. Four of them are from probably the 50s or 60s and one is new.
The older ones measured .0100", .0110", .0135"-.0140" and a very thick and stiff Russian leather at .0180. The new English leather is .0115".
The two I like best are the old at .0110" and the new one at .0115" which equates roughly to 7 oz. leather.
I too, am tempted to try Kangeroo leather for stropping.
It is very supple but it would be easy enough to pull it more taught when stropping to make up the difference.
Personally I would never treat my finishing strop with lather, neatsfoot oil, or anything else. Rubbing with the hand works well enough for me.
Good luck with your strop and good luck to you in your military service to our country.