I’m interested to hear a way to do this right that isn’t a lot of work for a 4 minute song!
For extensive discussion on how to do this, you may want to google search this forum for posts by vic_france and crotchety, throw the words “free-tempo” or similar in there to narrow down the results.
FWIW, I always do what you do - free tempo a keyboard recording, then apply MIDI parts to it. The way I do it is to :
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Create a tempo map that accurately follows the audio. I do use “Merge Tempo From Tapping” because the automatic tempo detection doesn’t work that well for my piano audio, but as you pointed there are other methods. I then tidy up the tempo map with the Time Warp tool so it exactly follows the audio.
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I then get the audio to play at a fixed tempo, temporarily so I can overdub MIDI. To do this, I apply the “Set Definition From Tempo” tool (after making the exact tempo map, above!), then deactivate the tempo track and put it at a fixed value, 90 or 93 beats per minute, etc. (i.e., at the tempo that the audio would be at without the nice free-flowing tempo variations). When the song is played back now, the audio plays at a fixed tempo.
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Now that the audio plays back at a fixed tempo, it is easy-peasy to overdub MIDI parts.
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Once I’m happy with the MIDI overdubs, I reactivate the tempo track, the audio will go back to its free-flowing tempo, and the MIDI will of course follow it.
Of course, if you don’t want tempo variations in the audio, you can stop at step 2 - the audio plays back as if it were recorded to a metronome.
Hope this is helpful!
[EDIT]
Just updating this thread to provide a link to a related one, with a little more detail: