I tend to aim for almanac guidelines. But I am more tuned in to your issue of how to handle heavy clay. Drainage is key. I subscribe to the school of growing above the clay, a la "no dig" gardening methods.

Two benefits. Your back will thank you, and you prevent the "soup bowl" effect that traps water and potentially drowns plants' roots. You can make formal raised beds, but more easily you can just layer amendments on top of the soil. Numerous no-dig videos exist on you tube.

Not since it was all my Grandparents had.....

Years ago I heard of the ancient farming adage "New moon supports beginnings/plantings, full moon supports endings/harvesting." It makes sense to me that throughout time, humans paid attention to the results of how they timed their gardening and results.

To deal with hard clay soils, I would recommend one or both of two things: (1) till in diatomaceous earth (gypsum). and /or (2) till in a significant amount of cottonseed hull mulch. After that, just keep mixing in added organic matter.

Weather will vary little year to year on average according to the lunar calendar, so most people that pay attention to weather cycles will look at the point you are in the lunar cycle to try and predict whether you are too early to plant or not. Again this is only the average and doesn't predict any single planting season. I also look at the long term weather forecast and whether my back hurts or not.

There is a whole village next to ours where the farmers plant and harvest by the phase of the moon, especially beans. It is some German historical method.

May I suggest adding a few 50 quart bags of Mirical Grow potting soil to your clay , before you plant anything ?