Two ideas to try.
If you get a ratcheting box wrench the right size, you can put it on the allen wrench almost flush with the plug
surface, shortening the allen shaft and giving good leverage.
I didn't find your photo
. If there is room, chuck a small engine
valve in a hammer drill, and hammer on the end of a section of allen wrench held in a needle nose, or better yet a needle nosed vise grip. That will vibrate the plug
without distorting the hole.The hammer drill will hammer, and the valve face will slip on the end of the allen piece while olightly pounding the plug.
I would try the soaking first, and the cool/heat cycles next, if possible. But several minutes of light vibration does wonders with rust, and unlike an impact hammer, you can vibrate for a long time without torquing on the plug. THEN try twisting the plug. Good luck.