Try a Players HXT shaft, 11.75 mm, about $100 with a Kamui Soft or $80 for a 12.75 version.
I have had 2 LD shafts I liked the hit of, a Mike Webb shaft that he made a couple of for a friend of mine, and the Players HXT shaft that's on my son's new cue. He has the 12.75 mm one, which feels thicker than that to me, but you can probably turn that down to a 12.3 or less, or go with the 11.75mm model which looks to be a bit over that anyway based on some feedback I got from other owners. They tend to be over the listed diameter a bit.
Those two shafts, after trying several 314 and OB models over the years have the closest match to a regular maple shaft. The OB had a nice hit to it, but felt a bit whippy.
The HST does not have a huge amount of LD properties, it's a bit in the middle range. Mike Dechaine tried it and missed two shots by a diamond when he aimed the same way he would with his Predator stick. But it does deflect less than all the regular shafts I use with my cue.