Nighttime batteries for Thinsats
Thinsats stop working when they go behind the Earth. "Thinsat night" for the m288 orbit lasts around 2400 seconds around the vernal and autumnal equinoxes. What if the thinsat had enough battery to keep functioning for that entire time?
A 4 watt thinsat requires 10000 joules of power storage. The thinsat is in daylight for 12000 seconds, so (with 83% conversion inefficiencies) an additional 1 watt of solar cell would be needed to provide the energy, perhaps 1 additional gram. The best batteries (Lithium Thionyl Chloride) store around 1.2 MJ/Kg, or 1200 joules per gram, so 10 KJ requires 8 grams of battery. So, to keep a thinsat lit up (at midnight on the surface underneath!) during the entire dark time adds at least 9 grams to the previously 3 gram system, in order to provide a little bit more night-time compute power, storage, and communication. The main advantage would be for communication. Adding 300% weight to add 20% more operating time is not a bargain - it is better to place more thinsats where they can be seen from the night-time surface.
Normal nighttime usage
At 45° latitude, 25% of the m288 thinsats are visible above a flat horizon. If 5% are too close to the horizon to see, and the center 17% are in shadow at midnight, then the percentage visible at midnight is small, only 3% of the entire constellation, 15% of daytime coverage. However, this may be enough for the reduced nighttime traffic. Alternately, existing higher-inclination services such as Globalstar may be used to increase coverage.
If m360 constellations are used instead, the ping time increases from 63ms to 73ms. The longer distance reduces daytime bandwidth (at the same power level) by 26%, more if latency matters. The nighttime coverage get better. 29% of the constellation is visible in daytime at 45° latitude, while 14% is blocked by the earth at midnight. With the same 5% horizon blockage, 10% of the array is visible at midnight, 42% of daytime coverage. So the overall effect on the system is approximately 26% drop in daytime, 16% better at midnight, compared to m288. For applications demanding minimum bandwidth 24x7, this may be a better tradeoff, but most human-oriented applications have peak usage during the day, and in the early evening hours.
For m480, the ping time increases to 87ms, 32%-5% or 27% are visible in daytime, 10% are blocked at midnight, for 63% of daytime coverage. Daytime bandwidth drops by 48% compared to m288, nighttime availability is 18% better. This is probably impractical.
These numbers are crude; the "close to the horizon" numbers especially. A better analysis is needed, probably by satellite amateur radio folk.