About monarchy: with 7 towns almost perfectly settled and courthouses/observatory 9, I had a total of almost 6.31 times what a single town would do, there was a few % of corruption in every towns despite the buildings (except in the town in the middle), it's very likely that 8 towns or more even perfectly settled is slower than this and actually the math is very easy for 6 towns which should give no corruption in any town (maybe a little but buildings can completely remove them): 1+1+1+1+1+1.3=6.3, so this is even better than 7 towns because the new towns don't slow you down until they have their harvesters/science buildings to the max and you also suffer less from corruption until you unlock the observatory which is far from medieval age in which you unlock monarchy. Also using treatises is better in that case. And in case you wonder: less than 6 towns can't be better than 5.3 so 6 towns is really the best. Now in the rare case where you spawned in a peninsula and thus would be forced to build your towns quite far from each other, maybe with 6 towns you would still have too much corruption, so I would recommend restarting a hero as soon as you see this, such case is that rare that it's unlikely that you will have to do the tutorial more than twice.
So to make it short: without monarchy you should make 4 towns and you will have a research speed of 3.0616 times what you would have with a single town without perks, with monarchy you should make 6 towns and you will have 6.3, I tried myself and once the observatory is built it allows you to research 2 techs per day, actually if I didn't sleep that much I could start doing that even before the observatory, nonetheless I researched the whole tech tree in less than 100 days.
Currently working on a better guide, also testing and researching , faster, more efficient research. Try everything, once , then try it, a bit different. }:-} Science victory, not yet released, but one day.........