Seems to me like it has a lot to do with ambient temperature. My brother had an escort (SOHC version, not the DOHC) that he had me exclusively work on because he's not anywhere mechanically inclined.
Just to make sure and verify, when you are checking the trans fluid, you have the engine running correct? Shifted through all gear ranges slowly, and ended in park, keeping the engine running when you checked it?
I recall you saying that the air filter was new, but had about 10k on it. that was the reasoning behind the air filter. depending on where you live, filters can clog up faster than expected.
You can try running premium, but on your engine, I highly doubt that it will help. Unless you have significant carbon build up, or have modified the engine to run higher than normal compression, premium fuel won't fix your problem. higher octane will give you higher power output only on an engine with high compression. The whole reasoning behind running higher octane is to prevent detonation when running higher compression, which can get more power than a low compression setup. Power would go down in a high compression motor on regular 87 octane gas (85 at high altitudes) due to the fact that it has to retard timing to prevent detonation. You can try it if you'd like though.
The 2.0 that is in the thing isn't the peppiest motor in the world. the throttle plate is pretty small too. the difference in temp *most likely* has a lot to do with it. Especially at night. Car's get much much hotter under the hood sitting under the sun, despite ambient temp. warm air has less oxygen, as you can probably tell by walking from heat outside into air conditioning inside. measure the humidity and it's about the same, but you can breath much better.
the extremely hot air results in needing a wider throttle opening to achieve the same amount of oxygen for the fuel burn. This translates to you needing to "Give it more gas" in order to get going to the acceleration and speed you want. You're not using any more fuel though, just a wider throttle opening to get the needed oxygen.
try tomorrow early in the morning and see if its still sluggish. then try again when it's hot out, then again when it's cooled down again. If it's powerful in the morning and night, but not during the day, chances are it is mostly temperature related.