This is the rock tradition, in which high tenor range in males (even falsetto) is prized, because it connotes passion, deriving from the gospel and soul singers emulated by singers like Paul McCartney and Robert Plant, which led to the mainsteam rock vocal style which is essentially screaming in tune.
And in folk/acoustic music there's Neil Young, who sings an octave higher than normal guys like you and I. Add Paul Simon, James Taylor...
Uh-huh: Leonard Cohen, Johnny Cash, Tom Waits....?
Nope, absolutely not.
But that's point. John Denver isn't singing it, you are. Nobody expects or wants you to be a John Denver tribute act. They want you to do it your way. You can't be a "failed John Denver". You have to own it, make the song your own. You have to do it in the key in which you can deliver it to the best of your ability.
Of course the song will sound different. That's
good.
Naturally, it's still possible that changing the key will somehow mean the song loses whatever magic it had for you. Maybe some essence of the song is not in its lyric, its melody or chord changes? Maybe it's in the fact that it's sung by a man with a high voice?
Personally I don't think would apply to a John Denver song, but there are some Neil Young songs where a big part of the appeal is that plaintive cracked tenor he sings them in. He sounds
lonesome up there, more than you will in that bass cellar you're occupying.
I mean, you can be lonesome in a cellar too...
so in that case, that would be the vibe to go far. Think about the emotional appeal that Cohen, Cash and Waits each have - each different in their own way. Make them (and similar singers) your lodestar. Cohen and Waits wrote their own material of course, but Johnny Cash covered lots of other people's songs, making them his own.