OK a few things:
1) The rule about not facing off the page, don't live by it. I break that all the time. If the page looks better with the guy looking off it, so be it. Don't do something stupid to avoid it just because you've been told to.
2) NEVER wrap boxes or game summaries over 2 columns unless it's part of a larger agate package. If it's pulled separate with a story, make the layout work with it. We have "standard" shapes for our college basketball boxes and minor league baseball box that are a little deeper than a lot of games need, and we use those to set our depth. Gives a good starting point, and if it ends up short, you get a few more lines of story or you just justify the shape. In fact, the only agate that should wrap over more than 1 column is a tournament schedule or tournament results or a wrestling dual summary or something like that, and even with those, unless it's a big file, try to keep from wrapping it. In most cases, if you're wrapping other agate that's with a story over multiple columns, you're doing it wrong.
3) Like everyone has said, get to know the program. If you want to go from being a paginator to a designer (and no offense, but most people at most shops just paginate; there is little time in most modern newsrooms for design), then you need to learn Photoshop as well, at a bare minimum. Illustrator helps, too.
4) When you start doing pages, learn what you know how to do and live in that zone, stretching out a little at a time. Don't try something crazy without a backup plan. See a cool cover from Omaha or Cleveland that has lots of cool effects and different type treatments? Don't try it. That's not your zone right now. The worst thing young and inexperienced designers do is try to do cool things with different fonts and typography when they don't have a feel for it yet. I did it myself. Too many times. Learn what you do well, and then expand your tool set from there.
5) How do you expand that tool set? A few ways:
-- Find someone at your paper who can look at your stuff and give you guidance before it goes to print and let you play with it. When I started at my current stop, I thought I was pretty good, but I knew there were a lot of folks better than me. Let them see your stuff, esp. the stuff you think is good. Because odds are either (1) it's not as good as you think it is (I speak from my own experience there) or (2) they can offer little tips that will help it reach the next level. So figure out who the best designer is at your shop and see if they'd be willing to help you learn.
-- Ask that person to critique you every week or so. Gather your pages and let them tear them apart. If they aren't ripping them to pieces, find someone else. You don't want someone who sugarcoats things and makes you feel good. You want someone who will rip your best page apart and make you see what it could have been. (The same can be said of writing; find an editor who will tell you just how bad that awesome story you wrote is; you'll thank them for it later.)
-- Learn from what other people are doing. Check out magazines -- I learned most of my typography skills from different magazines, which do type far better than a lot of newspapers. Go to newspagedesigner.com and check out the portfolios there. And don't limit yourself to looking at Sports pages. Check out the news and features pages, too. You may find something -- a way a photo is played, typography on a headline, etc. -- that you want to use.
-- Don't steal designs. That's visual plagiarism. But don't be afraid to be inspired by them.