I made a VERY solid crossmember out of 2x8x1/4 wall rect. tube. VERY simple, it took about 2 hours to make. The tranny mount sat on top of the crossmember just like factory. I just drilled 1-1/4" access holes to get to the 4 tranny mount nuts. I angle-cut the ends so I could get into where the factory bolt pattern was on the frame rails. Sat the whole Jeep on that crossmember a few times, with NO issues.
Your design looks good, but 14ga steel sounds thin to me. I would say it would be OK if you made a rect box with the 14ga and the 1/4 strap as the sides, and bolted the tranny mount like factory, but if your just planning on bolting through the bottom layer of 14ga, my feeling is it won't handle a hard hit.