Just as a "devil's advocate brainstorming exercise", it sounds to me like your big competition is the Stickies type programs. To me a bad weakness of index card only size is once you get a tad above that size frame, you are stuck. Stickies can print on whatever size paper your printer can handle.
So for example, since the "search" was something I never do, I just checked. Let's consider Tom Revell's Stickies.
R-Click the small tray icon/manage stickies, then
... finds them by title.
Then for printing,
Properties/Paper Size and choose 4 x 6 or 5 x 7 or whatever your size is.
or whatever, because once you get into the print menu, it seems to be local firmware that changes a little.
Meanwhile, there's 3.5 levels of urgency. Use a desktop splitter like the one I use from the obscure non-Nany C contest here, Trandesk. You open Stickies on the 4th tab, with any one open, minimized, or long-term-closed as you like. Then splits 2 and 3 hold working projects, with their sets of stickies open or minimized. You save your last tab for the rest of your faster disposable stuff.
So put another way, a problem I see that you have to find a clever UI for, is "overloading" your app. Once you get more than about 20 index cards going, how do you deal with them?