Using Civi to track Major Donor and Grants cultivation

I’d like to pose a question to users of CiviCRM that is not particularly technical.  It’s more to do with using the existing features of Civi in the most effective and efficient way to do 2 very important things...cultivate Major Donors and apply for Grants. 

A team of fundraisers at a small-to-midsize nonprofit wish to track the process of identifying and connecting with a few hundred people a year, engage them (calls, meetings, events, tours, thank you's), and ask them for higher level gifts. They would also like to track this process for solicitation of Grants and Sponsorships (points of contact, submission and reporting deadlines), which adds another layer of complexity.  To be clear, this is not an RFP.   We'd like to share what we're doing and learn what you're doing.

How do we use Civi best to track Major Donor processes?  Well we've already begun using Activites to track "moves management".  We can easily add new Activity Types and assign these activities amongst staff.  Custom data fields allow us to jot down notes and tick boxes indicating results.  This is a handy way to keep track of what needs doing and avoid overlap.  Have others done the same thing for Major Donors?  What are your lessons learned and mistakes you suggest avoiding?  Please share your stories.

For Grants and Sponsorships, however, it’s a bit more complex, and not all of this grant application stuff is easily tracked as “Activities.”   I'm wondering what others have done before with incoming Grants, and how?    Is there an extension or setup that’s pre-made for this type of thing, but we’re currently unaware of?  Insight, experience and tips are welcome, thanks so much!