I appreciate the input and I hear you. The challenge is the balance between sports team rosters and general tables. I picked three formats - high-school, college, and pro - that seem to be very common on websites worldwide. (And I really looked worldwide because the plugin is used worldwide in several languages.) There are a couple of good general plugins. I have found that they are very flexible, very powerful, and therefore a lot of work to build and maintain. More work to build and maintain that 'volunteers' who aren't WP experts, or even computer-savvy, can take on.
As for the rosters, your links should look something like:
and right now, they look something like:
That's weird. You might try setting your permalinks to post name, which is what I use on http://shoalsummitsolutions.com/dev/ (a site which may help you debug if you haven't looked at it already). Your permalinks with the "?true=" make me think something weird is going on there. I certainly never coded something like that, but WP can have a mind of it's own sometimes. (You can turn those links off in the admin panel.)
Finally, I'm not sure what you mean by "the text field on the player definition page"?? I think all the fields are field on the dev site above and that I use all the formats, but if you can be a bit more specific I will certainly double check. (Could be the first bug ever! LOL)