Sounds like you have gotten to know your landscape super well, that's awesome! I have a couple ideas for you, so this may get lengthy, I apologize in advance
Option number one would be a couple of fixed schedules. You can set start and end dates for fixed schedules, so you could create one schedule from Jan 1-Feb 28, one for Mar 1-April 30, one from Jun 1-July 31, and so on. We run into some issues with the requirements for the rain skips.
Rachio's rain skip feature looks 24 hours in the past, and 24 hours in the future, and if the observed or predicted precipitation exceeds your selected threshold, it will skip. So that doesn't work exactly how you are wanting . Our climate skip feature takes a more holistic approach to weather, and will look at the past seven days and the next seven days and evaluate multiple different factors and how much they will deplete your landscape's moisture. If it looks like the schedule can make it to the next watering, it will skip. I would guess that this would satisfy the rain skip requirements you laid out, but unfortunately you can't explicitly lay out those requirements. The only way I could think to do those skips based on amount of rain would be to manually set rain delays in the app based on how much rain you observe.
Another option would be to switch to our Flex Daily scheduling and take the leap. You seem to have a very good understanding of your lawn, which puts you many steps ahead in setting up flex. Flex keeps your watering durations consistent, and just adjusts frequency based upon your local weather and zone settings. It looks like you are using the same logic, and manually adjusting for typical weather changes. I wouldn't be surprised if flex actually matched your above expectations, but without requiring multiple schedules. Accurate zone settings are the key to an effective flex schedule, so if that's something you would be interested in, let me know and we can double check those settings. Flex can react to weather in real time, so if you have a particularly warm July, and the schedule you outlined that you used in the past isn't cutting it, it will compensate for that.
I linked some support articles in my response, definitely check those out if you would like a more in depth explanation of some of the features I talked about. If you want to let me know which route you would like to take, I can give some more guidance on how to get it all set up!