An 1/8in will handle the forces, but would require frequent support points (every 2-3 inches) to keep it from flexing and vibrating. 3/16in would let you increase the span between support points, maybe to 6 or 8 inches.

I've used the M&K bellcrank on two pattern planes, and I can't recommend them. The need for supports to keep the rod from vibrating and flexing is a pain to install, and both of mine got sloppy with flight time. The fit of the two halves start out pretty tight, but the plastic spreads where they join and after a couple of years gets a couple of degrees of slop. Having the two elevator sides varying a couple of degrees is huge in pattern.

I switched to the DEP system and have better experience. It uses continuous support, and there just isn't any place for slop to occur, except where the clevis's attach to the servo and elevator. Price is about the same. When you look at DEP, it looks like more work, since you must build this support ladder, etc. Maybe for the first build, it takes more time to figure out, but once you do one, it gets easier. Plus the bellcrank has its installation problems also. For example, if your fuse sides are not parallel where you are mounting the bellcrank, and most are not, then the bellcrank won't mount flush on each side, and you end up making shim pieces to go on each side so the bellcrank can mount parallel. Also, trying to hook up that long rod to the bellcrank back there with the narrow spaces can be a bear. I've had to cut a hole in the stern bottom to snap on the long rod clevis not what I wanted.