I suggest a fourth possibility for Sanhedrin to consider: an eternal calendar based on round numbers; (year - 3600) / 480. Here is the complete program.
Output for the years 5790 + n*19, up till 6200:
5790: 49-03
5809: 48-03
5828: 48-03
5847: 48-03
5866: 51-03
5885: 50-03
5904: 49-03
5923: 50-03
5942: 49-03
5961: 50-03
5980: 49-03
5999: 51-03
6018: 20-03
6037: 20-03
6056: 21-03
6075: 21-03
6094: 22-03
6113: 21-03
6132: 21-03
6151: 21-03
6170: 21-03
6189: 20-03
Here 49-03 is 18-04, et cetera. Note how this does not "allow" the dates 18-03 and 19-03. Here are the first two cycles after 5782:
5782: 47-03
5783: 37-03
5784: 26-03
5785: 44-03
5786: 33-03
5787: 23-03
5788: 42-03
5789: 31-03
5790: 49-03
5791: 39-03
5792: 27-03
5793: 45-03
5794: 35-03
5795: 24-03
5796: 43-03
5797: 31-03
5798: 20-03
5799: 40-03
5800: 29-03
5801: 47-03
5802: 36-03
5803: 26-03
5804: 43-03
5805: 33-03
5806: 22-03
5807: 42-03
5808: 29-03
5809: 48-03
5810: 38-03
5811: 28-03
5812: 45-03
5813: 34-03
5814: 24-03
5815: 44-03
5816: 32-03
5817: 20-03
5818: 40-03
5819: 29-03
