Multi-round Transposition/Playfair as a secure hand cipher in the computer age
Some years ago, someone (Terry Ritter maybe) suggested using Playfair as follows. 

First: just normal Playfair with some key.
Second: add a single null at the front and at the end of the cypher text.
Third: go to First with new key.

This can be extended by repeating the process. The point of adding the nulls is to split letter pairs between rounds. You could improve it as suggested in your question by using a transposition cipher before the Playfair step. Computer attacks on Playfair often just exhaustive key guesses coupled with Playfair's lack of ability to diffuse the key through the plaintext. Transposition breaks up the keyword search and adding single null between steps increases diffusion.

Still, one needs a fairly long key for the Playfair part. Perhaps using parts of a shared book keyed off the date. (Bible, "Catcher in the Rye," "Texas Almanac," etc.)