Meditek, The short answer is, No, I don't think so. If I'm wrong about that, I'm sure Sara will pop in and correct me.
Running the search as often as you want, kind of implies you're looking for an auction that ends soon. Not only the new items that end 7 days from now.
I think you may be happier with eBays email. Yes, it only runs every 24-30 hours, but most auctions last 7 days. That still gives you plenty of time to consider bidding. Also eBays search is a little more flexible and more complicated searches can be entered.
Other than the frequency of emails, eBay does what you are looking for. (both A and B in your post) **A note for if/when you test the eBay email. If you do a manual search from the 'My eBay' page, I believe that resets the 'Once A Day Clock' back to zero.