In LRO-H2, I use a cantenna as my waveguide, and aim this at the dish, rather than out into space. Does the presence of the dish change the ideal dimensions for the cantenna and position and length of the monopole inside it?

Short answer: No—the dish doesn’t change the waveguide dimensions of the cantenna.
The can’s internal diameter and the probe/back-short geometry are set by your operating frequency and waveguide mode, not by the reflector. What the dish does affect is the required beam pattern, edge taper, and phase-center placement of the feed.

What stays the same (set by frequency)

Treat the cantenna as a short section of circular waveguide excited in TE₁₁:

• Diameter (d): choose for single-mode TE₁₁ at your frequency (f).
  Cutoff for TE₁₁: ( f_{c,11}=\dfrac{1.8412,c}{2\pi a} ) with (a=d/2).
  Practical design: pick (f/f_{c,11}\approx 1.25\text{–}1.35) while keeping higher modes above (f) (e.g., (f<0.85,f_{c,21})).
• Probe to back-short distance: about (\lambda_g/4), where
  ( \lambda_g=\dfrac{\lambda_0}{\sqrt{1-(f_{c,11}/f)^2}} ).
• Probe length: start near 0.2–0.25 (\lambda_0) (trim for best match).

Example at 1420 MHz (H-line)

• A good starting diameter ≈ 160 mm (single-mode, TE₂₁ still above band).
• (\lambda_0) ≈ 211 mm, (\lambda_g) ≈ 330 mm, so back-short ≈ 83 mm past the probe.
• Probe length ~ 40–55 mm (then tweak for return loss).

These numbers don’t depend on whether your dish is 1.0 m, 1.5 m, or 3 m.

What does depend on the dish (pattern & placement)

Your 150 cm dish mainly sets how the feed should illuminate it, not the internal waveguide sizing:

• Edge taper: choose the feed so that the field at the dish rim is about –10 to –13 dB relative to boresight (helps spillover/noise vs. efficiency).
• F/D matters: the required half-angle to the rim is
  ( \theta_{\text{edge}}=\arctan!\big((D/2)/F\big) ).
  Pick/shape the feed so its pattern hits ~–10 to –13 dB at (\theta_{\text{edge}}).
• Phase center: place the cantenna so its phase center sits at the dish focus. For a plain open circular guide, the phase center is a bit inside the aperture; adding a short conical flare or scalar (choked) rings can improve edge taper, reduce spillover, and pull the phase center forward.

Practical tips

• A bare cantenna often has a pattern that’s either too broad (spillover) or not tapered enough for common F/D≈0.35–0.45 dishes. A short conical flare or scalar rings can nail the –10 to –13 dB taper without touching the can’s internal dimensions.
• Optimize S₁₁ at the bench (VNA) by small adjustments of probe length and back-short distance, then adjust feed position at the focus for max aperture efficiency on-sky (Sun/Moon Y-factor helps).