I have never understood where in Preferences the latency settings are for playback and recording. They're confusing. Anyway...
 
I have installed X3e on a new computer and am trying to set everything up the way it was before. I open a brand new file and record midi, and there's no latency at all. But I open a very large file that I built on the old computer, and there's about 0.3 seconds latency on recording. This is true for any instrument or source. On the old computer, which was a much poorer machine, there was almost no latency on recording. 
 
Why has this old project suddenly introduced recording latency, but there is no such latency on a new project?

Plugin Delay Compensation
 
Some plug-ins require a lookahead buffer to work properly
 
This means the project playback must be delayed in order to keep everything in sync.

That is not it. This project (or any project) didn't have this problem on the old computer, using the exact same plug-ins. Some Sonar setting is set back to its default that had been adjusted in the old version.
 
Also, and probably more importantly, this delay occurs no matter what instrument I am using. And only with this project that worked fine on the old computer. New projects do not have this problem.

Did you try the old project with a bypass of all effects before concluding that plugin buffers are not involved? Most sonar settings are global to the program and if it were just one of those settings causing the problem, you would expect it on all projects. I am not clear on what relevance the instrument you are using would have on this issue. A lookahead buffer is going to initiate a delay even if it is not on any track using an instrument. So a delay buffered effect on an audio track has to slow down all of the tracks (including MIDI) in order to make them all line up in time. 

Figured it out. 
 
Audio > Driver Settings > Mixing Latency
Slide the suffer size to the left ("Fast") as far as it would go without distorting the sound.