How to keep up on Science on Immortal?

Preamble:

I don't care for direct science victory as a primary objective, however; I do realize the importance of science for the game. On Emperor I have no problem keeping up on science against the AI (I'm almost always 1st or 2nd in demographics), however; on Immortal I have issues keeping up.

My Play-Style:

My typical priority for a city (generally I keep by this with a few obvious exception cases):

Build available food buildings
Build a worker if needed
Build available science buildings
Build military units if at war
Build buildings specific for that city's strategy or civilization's strategy

I get my worker building farms immediately, I go for writing ASAP, and I build libraries as soon as possible. The only other way I know of possibly preventing this lag-behind is building the Great Library or Capturing the City that has it.

I don't always immediately go for the National College but I get it relatively early-on.

I'm always in last before I even get the chance to get Rationalism. I don't usually settle in Jungle heavy areas nor do I build trade-posts abundantly so I doubt Rationalism would save me from this seemingly inevitable doom. What can I do to avoid this?

Question(s):