I have a table of simple lat/lon values in decimal degrees in an excel spreadsheet. I have no problem importing and converting it, and it claims to be in the right projection. But when I open it, the projection is WAY off to the southwest. I cannot figure out any way to fix it.

It is a geographic coordinate system, perhaps GCS WGS84 or GCS NAD83 perhaps.

Was Longitude chosen for the X axis and Latitude for the Y?

I would check that you used the Define Projection tool, to define the actual coordinate system. Excel know nothing of this at all.

If you need it in another coordinate system, then you have to use the Project tool, which will produce a new file in that coordinate system.