Thanks again. I was able to manipulate your instructions a little bit to make sure this doesn't break through subsequent upgrades.
I'm only posting this in case this helps other users.
I already have a stylesheet being referenced in my master pages, and we have MANY master pages across various sites. So I didn't want to have to go add a new <link> tag to each one.
So, I opened up the one stylesheet they all reference, and added an "@import" line to the beginning of it.
That line looks in the "/_layouts/<rest of my path here>" folder where the current stylesheet is housed.
Then I altered the RadEditor's ConfigFile.xml to look at that same path using just "/_layouts/<rest of my path here>/MyNewCSSFile.css". This worked great and it won't break if we upgrade the RadEditor and the path changes to something other than "/_wpresources/RadEditorSharePoint/5.x.x.x__1f131a624888eeed/Resources/".
Another question I have, still concerning this, though:
When I apply one of the styles you suggested, like ".purpleTable", inside of the Table Properties window, how does it get the classes written to the table automatically? As in "purpletableTableHeaderRow" or "purpletableTableHeaderFirstCol". Will it always automatically add the <whatever>TableHeaderRow class, no matter if you've declared something for TableHeaderRow?
Or maybe a better way to phrase the question is:
How do I just apply styles for alternating rows and not have to code for the HeaderRow and FooterRow? Because if I remove the CSS styles for HeaderRow and FooterRow, it does not grab the normal Odd and Even row styles. It just keeps the HeaderRow and FooterRow without styling.
Thanks for all your insight so far!