Well the AI is epically stupid and boring, I really don't see the point in discussing strategies vs such an opponent. Although what is more efficient in a multi-player game should also translate over to a single player game.
Except of course for unrealistic stuff where the AI makes GL on turn 15. Since the AI can only be competitive through blatant cheating, single player is wholly uninteresting IMO.
It's like discussing how to beat a chimp and then oh wait, the chimp has a laser gun while you have only your fists. Yeah, hes completely stupid but has a massive advantage if he can figure out how to use it. This is single player mode.
this made me laugh

i too play almost exclusively MP, since single player is unchallenging. not only that, but deity games limit your strategy (units such as rome's legions become useless for offence since they come too early and at this point you have a huge tech disadvantage)...
anyway to the point of this thread: liberty is either underpowered, or tradition is massively overpowered.
adwcta, you can say you crunched the numbers all you want, i say you crunched them wrong. you probably left out important stuff out, if you reached the conclusion that liberty is better at larger empires.
this game has so many variables in it, the easiest way to know tradition is OP is playing a wide 8 city empire with tradition and then another one with liberty, and see which one goes more fluintly.
to every one of liberty's bonuses, tradition gives a better one. to every one of its free stuff, tradition gives "free-er" stuff. +1 hammer and +5% prod with buildings? HAH! tradition has +2 food and +15% growth. early on thats another hill (+2 prod) later on thats 5 extra citizens and 3 more hills.
1 free worker and 25% worker speed bonus? tradition has 160 INSTANT hammers with monuments (that generate culture INSTANTLY. no need to wait 20 turns to finish the moneument, that adds up to some heavy culture early on).
the tradition finisher is ridiculously good, due to:
1. the aqueducts being FREE and INSTANT. that means by the time liberty has to research and build those things, which can take more then 50 turns extra, this finisher grants the 4 tradition cities several new citizens each.
2. you dont have to research them, which lets you focus on universities etc/ upper part of tech tree.
3. they are FREE. they dont make future aqueducts more expensive, like the liberty finisher does.
i can go on and on, but honestly other people have summed it up better then i have.
play ninakoru's balance mod if you want a balnced SP game.
in short, monarchy needs a big nerf, and traditions free stuff need to apply to 2-3 cities instead of 4.