there are certainly better LDOs which can do nano amp quiescent current such as AP7354-33W5-7 but they are of course a bit more expensive.
is there any real gain from switching the LDO to a better one with lower Iq? or would it be just an overkill.
Well, you would come close to doubling the life of the battery. The better LDO will cost four or five times as much, but still not a lot of money in absolute terms. So I guess it depends on whether you will be making a million of these devices, or just one. The MCP1700 is another one you might look at that might be more readily available.
your suggested MCP1700 is very good. ground current is about 4 uA and quiescent current about ~2uA so total would be < 6 uA compared to 29 uA from before. it is 3 times the cost though but still good enough as the board will not suffer from < 0.3$-0.5$ price increase.
I will make say hundreds and sell them, in batches according to demand.
However, in this experiment I am doing, I am seeing if the cheap (and still very good) LDO of 29 uA will be that much effective or not.
if we assume total current consumption from everything is just about 60 uA total, then what will that be for a 18650 battery? my assumption is that it will be literally nothing. if so then changing the LDO won't be much of a change.
yesterday at this time it was 4.112v and now it is 4.110v so a 2 mV drop which is less than before where it dropped by more than 5 mV, and very early was more than that.
to my understanding from explanation above about chemical characteristics... this should be normal and will settle at some point, after that will be mere self discharge + my 50-60 uA which in reasonable assumption won't be dropping battery voltage in any effective matter.
I would be very happy if the battery will last for a year, which by all reason and calculations it should do much more than that.