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Finance and fundraising often find themselves with these kinds of confusions. It can help to look at it from the others perspective.
Fundraisers think about contributions based on the way they approach the donor. They aren’t writing a grant for DAF (or small family foundation) gifts the way they would with a large foundation.
I work with several nonprofits using QuickBooks, but whatever general ledger software you use will most likely have a similar functionality. We have a specific service item for donor-advised funds that points to a Donations Directed by Individuals account. By creating services that match the things the fundraising department tracks, while pointing them to accounts that are meaningful to finance, you can make everyone happy. You can even get in the habit of running Sales by Product/Service reports, filtered for the ones you use for Contributions, to tie out and reconcile between the two systems.