Kaydia
Hi Kaydia,
I took a look at the song and I know what you mean with chords and notes sharing the same keys.
I googled some and found another version of "Leaving on a jet plane" on musescore. Please see the link below at which you can at least see the first page without purchasing.
https://musescore.com/user/39593079/scores/16041196
This is actually page 232 from Hal Leonard "The Real Pop Book", Volume 1, C Instruments, the whole song has 2 pages.
You can see that the Hal Leonard version is 7 steps up from your version. That might give you the separation that you are looking for. Specifically, the melody would be raised a little (by 7 steps) while allowing a little more room for the chords underneath so that the chords don't sound too dark.
Which brings us to the wonderful topic of singing the tune to the song while you play. The reason why I mention this is because a singer has an overall singing range and a preferred singing range. In my case, I can sing about D2 to C5 of which D2 to C4 is in chest voice and D4 to C5 is in head voice. My preferred range is approximately F2-C4. Thus when I look at a song, I take note of the highest and the lowest note in the melody. I then shift the song as many steps as needed to bring it within my preferred singing range. Shifting can be done either by finding written sheet music in my preferred key or transposing automatically on a keyboard. Ultimate Guitar has many chord charts that can be shifted exactly the way you like. Btw, some players can do shifting on-the-fly, because an acoustic piano does not have that transpose function. Btw, because I am a bass singer, I often need to sing 1 octave lower than the actual melody (although shifted to fit my preferred singing range).
The reason why I mention all this is to say that in our band, the person who sings the song gets to decide the key in which it is played, so the singer is able to perform the song. Then, the various instruments including keys adjust to that. The choice for keys is then to play in that particular key, or in a different key using transpose (if that works out better). Regarding this particular song, I would probably opt for the Hal Leonard version and shift that via transpose to whatever the singer needs.
Just for completeness, there are several ways of keys playing/singing. Playing the melody and chords is for example great for making music with a small group. The advantage is that the singer/audience has a melody to latch on. In our practice group with lead/rhythm/bass guitars, drums, etc. we often do not play the melody on keys, but instead something that complements the singer or provides accents, or a solo.
Anyway, just some more food for thought. All the best.