Precession

The Venus / Earth metonic is 8 years. It has two leap years in there. (Usually. We'll get to that.) Earth's position on its orbit - its sidereal angle - may be expressed in Earth calendar days. Preferably with more Leap Days than the Caesars proposed, so: anti-Gregory. Earth's position relative to Venus is just another day, and this day will differ even when they "meet up" again after the metonic. This has implications on relative angles and (mostly Earth) eccentricity. In short, Synod A's budget for Venera 4 in AD 1967 will not be the same in 2047. Every 96 years is 12 metonics. So, let's ask a Babylonian to look into how the schedules shift.

Based on the Stjerneskinn almanac, we can use Inferior Conjunction: 12 May 12:00 UTC AD 2100, 14 April 10:00 UTC in AD 2196. Earth's position relative to Venus falls back 29 days and 2 hours. To round out the century, it falls back 30 days and 7 hours.

Every 400 years is a leap year again. Superior Conjunction (i.e. opposition) 11 June 10:00 UTC fell to 15 May 1:00. Obviously this fell less, 27 days and 9 hours. Round off that century to 28 days and 15 hours.

Take the first three centuries together for 90 days / 21 hours; then add the fourth for 118 days and 36 - that is, 119 days and 12 hours.

153 Earth/Venus metons for 1224 Earth years should take us to about a full return. Luckily for Hard SF authors, it's a pentagram. Even luckier: the 243 Julianesque year (plus 2-3 days, by Gregorian year) span marks the Transit Cycle. We confirm Gregorian with the "Superior Conjunctions" 1 May 1901 (observed 30 April) and - predicted - 2 May 2144 / late 29 April, 2152. Compare Hop's schedule: 2005.7927 (E, like Mariner 10) with 2232.8022 (B) down at the end. For B, it doesn't take much extrapolation to predict 2248.789. This is all very rough for me but then, it was rough for Hop before me. I must, though, trust the almanac more ... and the transits most.

From Venus' side, that's 395 of her sidereal years.

Pope Gregory's equinoxes are his problem and (to a lesser extent) the Greeks'. Venus' problem is to fit 151-2 five-synod metonics into 1215 Earth sidereal years. Maybe lose a synod from meton #152? or a half-synod Hohmann orbit?

Ah, there's over a millennium to figure that out. I suggest to compare 9 November 1973 (E) with Hop's 2168.8558 (B); January 12 1969 (B), with 2196.0330 (D). If you - the Babylonian - are calculating delta-V budgets, and you're looking to the historical period such that the 1967-73 table will make sense again: AD 2168 is as early as you should start. I'd lean more to AD 2210, myself.