Hello Andy and other readers.
An interesting project.....but I want to make sure that you're not presuming that a probe forming a waveguide-to-coaxial transition needs to be a quarter wavelength long - it's usually better not to be so.
Apart from off-the-shelf transitions made by the likes of Hewlett-Packard (e.g. X281A), the best-matched 'probes' that I have seen are not just straight 'rods' but they look more like inverted cones with the broad end in the middle of the waveguide. And they're not a quarter wavelength long either. I have done some trial-and-error experimentation and have confirmed that probes like these have worked very well in various projects. I remember one case making a probe of increasing diameter using several pieces of brass tube of incrementally increasing diameter. (Sorry, you can't work in waveguide and avoid some metalwork!)
And being a little shorter than a quarter wavelength, it is intuitively allowable for an adjustment screw to be introduced through the opposite wall, adding a little capacitance there. But adjustment screws may need to be better placed at another location and the old trick of leading a small ball bearing around inside by way of a bar magnet held on the outside, is a great way to find where the 'sweet spot' actually is.
Approaching from another angle, a very good way of bringing any trial-end-error waveguide transition into submission is to have a close-fitting back short, the position of which is adjustable by sliding in and out a little. Known good directional couplers (waveguide and/or coaxial) are your friends here!
Just a few comments to start.....
Cheers and 73,
--Doug Friend, VK4OE.
p.s. I originally sent this as a reply to the reflector about two hours ago, but I never saw it sent out - no explanation. There was essentially no procedural difference between that message and the one only minutes before in which I described a possible place to acquire the likes of an M57762 which did make it to the reflector. So this time I've generated a direct posting to the reflector, copying the original.