Let's do something really radical.
Let's translate a melody from one idiom to another.
We have a tune in 3 - 4. We want to convert it to 4 - 4 swing.
We retain the natural accent.
We transcribe one measure of 3 - 4 (with careful massaging) to one measure of 4/4.
We retain the pulse of the song. eg An 8 measure verse in 3/4 transcribes to an 8 measure verse in 4/4.
We ensure the melody's natural accents fall in 4 - 4 roughly the same as they did in 3 - 4. So even when the melody is transcribed into a new time signature, the natural pulse is retained.
The melody is underneath.
Quavers swing, so we want plenty of quavers in our transcription.
From 3 - 4 to 4 - 4 we have an extra beat to make room for. We can greater emphasise the 5th note by anticipating it (playing it before the beat). Notes 3 and 4 can be played crotchet - quaver or quaver - crotchet. Using the first approach the relative upbeat / downbeat importance is retained.