Good News: No need for spacer or shim
I tried small shims, small washers, but everything thing I tried, were still making the battery protruding the body a little bit, very annoying. So I decide to work on the actual IMR cell's protective plastic sleeve around the button.
I used a hobby knife to cut away the battery cover around the (+) button, leaving just a little bit to wrap around the (+) end assembly (which should be enough to hold the components in place). Put the improved AW IMR cell into the T1A, screw back the tailcap. And - bingo, the light lit up. :twothumbs
The new light output from an IMR16340 cell is about the same as a fresh CR123. So I don't think the Seoul P4 LED is being over-driven. I hope the buck-boost converter SF designed is able to cop with increased in voltage from 3V to 3.7V. (Note: P4 has a forward voltage Vf between 3.25V-4.0V, so Vin of 3.7V is not that high really. However, use rechargeables at your own risk)