Don't panic just yet!
Firstly, using prehistoric toeclips isn't helping, so make the effort and try some SPDs. You could pick up some for next to nothing on Ebay to try:
http://cgi.ebay.co.uk/SHIMANO-PD-M520-SPD-PEDALS_W0QQitemZ230195979910QQihZ013QQcategoryZ36137QQssPageNameZWDVWQQrdZ1QQcmdZViewItemfor example
Then once you have seen the light (after the inevitable one fall - try and find somewhere soft..) get some of these:
http://www.sjscycles.co.uk/product-Shimano-Shimano-PD-A520-SPD-pedals-11394.htmWhich are a match made in heaven for your new bike. You'll need shoes that take spd cleats, but most modern cycle shoes do.
You can adjust the cleats fore-and-aft which will allow you some control over your overlap issue, but you'll probably find that adjusting the cleats so that they are under the ball of your foot means they'll work just fine for real world riding.
It's not often you have to turn the bars 20 degrees - get out and ride a few miles and you'll probaly find the problem evaporates. Just bear the limited clearance in mind for tight slow speed manoeuvring.
The 853 is intentionally tight at the front end - too much so for my taste compared to the relatively relaxed back end - but a lot of people swear by them. (I swore at mine and replaced it with a Cyclosportif but that's another story..)