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While I could generate any arbitrary gear ratio using that sort of technique, it would require unique spacing for every gear combination, produces very large gears, and doesn't satisfy my additional constraint that the sum of the two gears must match the sums of all of the other gears in the systems.  The last requirement comes from sharing the axles between all of the gear train stages.  I do have flexibility in choosing this spacing, but am limited in the total number of teeth for manufacturing reasons, so I wrote a tool that exhaustively searches the spacings to find the ratios that are closest.

For instance, the sinoid period of the moon is 29.530 days, so it essentially needs to be almost a 30:1 step down from the carrier rotation speed.  That is not easily achievable with a single stage (the smallest gear needs at least 10 teeth, and a 300 tooth gear is unreasonable), so a two stage gear box is necessary.  Limiting the search to a spacing of up to 150 teeth found that the two stages of 19:100 and 18:101 produce the ratio of 100/19 * 101/18 = 29.5317 days (which is pretty close!) on a common axle at 119 teeth spacing, and places the output gear for the moon on the same axle as the earth.

Mercury and Venus have sinodic periods of 115.8 and 583.9 days, but their sidereal is less than an Earth year, so they need to turn "backwards" on the Sun's axle from the Earth's perspective. They can use the first stage of the Moon reduction, as long as they reuse the 119 tooth spacing, and for the third axle the tool can search again up to 150 teeth spacing.  What it found is that a two stage reduction of 17:102 and 27:92 from the moon's first stage results in a 107.6:1 intermediate, and then uses that with a 65:70 for Mercury produces a 115.8:1 ratio, and 21:114 for Venus results in 584.1 ratio (on a common 135 tooth spacing).

Mars, Jupiter and Saturn have longer sidereal periods than an Earth year, so they need a reverser to turn "forwards" on the Sun's axle.  Another exhaustive search found combinations that shared the 135 tooth spacing, with an assist from the intermediate stage on the Mercury/Venus reducer.  Somewhat surprising to me is that Mars is the "slowest" of all the planets in the geocentric solarsystem due to its sinodic period of 779.9 days, so it has the largest gear reduction compared to any of the others.