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Funnily enough I have a suite of perspectives with radar in the name that serve exactly this purpose.

I have:
- short range radar views: flagged or due and available - with various sort options.
- long range radar views: remaining - with various sort options.

Every morning I have a quick glance through them all to see what's looming.

Omni are brewing a forecast view for the desktop version, but I guess we'll have to wait and see if it goes beyond the limitations of the iPad version that you detail in your post.