Counting items using criteria from 3 columns

Before I get into the challenge, there's a slight wrinkle—which is that this spreadsheet must exist on EditGrid. That's going to limit creativity, but I can see how it's a better solution an emailing a spreadsheet around.

In the attached spreadsheet, there are 3 columns and to the right of it, there is a small results table. I'd like to count the number of open and future reqs for each department. I used COUNTIFS for a similar Excel spreadsheet but EditGrid doesn't support the formula and these aren't exact matches! The req "numbers" may not always be numbers so I've been trying to figure how I can use COUNTA—I just haven't been able to nail down the logic.

Any tips and advice would be appreciated! Thanks.