I've been pondering a variant that probably needs some tweaking, but I think might be interesting. The idea started when I saw the title of Gozpels "Slow Motion is our Potion" game, but really has nothing to do with the variant there.
We Think in the Long Term
1. Tech Research - The only thing you are allowed to click on the tech tree is techs that have no direct follow on techs. You can only change when you get the "Pick a new Tech". And then only if you have reached the target tech that you last selected.
AA: Construction, Currency, Republic, Literature, Map Making, Monarchy, Horseback Writing
MA: Free Artistry, Music Theory, Theory of Gravity, Economics, Navigation, Magnetism, Military Tradition, Chivalry
IA: Advanced Flight, Amphibious Warfare, Sanitation, Ironclads, Facism and Communism
MT: Stealth, Recycling, Integrated Defense, Robotics, Genetics
2. You can only issue orders every other turn. You can issue goto orders and things like that which will span your next turn, but every other turn you have to just click "Next Turn" without adjusting anything or making any changes. (Or even canceling moves that are going to turn out badly)
Optional rules to add to the theme.
1. Sliders - You can only change sliders every x turns (10 or 20 sounds good to me)
2. Diplomacy - Player initiated Diplomacy could also be restricted to certain turns (every 10 or 20)
3. No Build Switching. You start and finish everything. (Could allow the exception if you get beat to a wonder, or you could say that that means you have to throw away the shields)