What is the best way to handle deprecated functions?

I don’t see anything wrong with your approach. But I’m going to take a different track: don’t support older versions of WP.

The general impression I’ve gotten from the WP community is one of progress. By supporting the current version and forward you’re helping to push the community towards using the most up to date version of WordPress.

Excerpted from WordPress Plugin Development (which is a great book!):

In the WordPress development community, backward compatibility may
sometimes be even looked down upon. Users are expected to stay updated
with the latest version of the software.

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