That's where inversions come in handy. However, any time you change the key to a song, the feel of the song becomes different, often in subtle but noticeable ways to those with good ears. This is especially true when the song is originally played with open chords. As soon as you play a barre or inversion, it's immediately obvious to all but the most tone deaf people that "something's not quite right" with the song.

A game several of us musicians used to play (many years ago) was to listen to a song we were not familiar with and determine the key simply by listening. It's really not as hard as it sounds. I find myself playing the solitaire version of this game even now.

All that said, good musicians can play a song in any key and make it sound good. As you point out.... Bad Moon in D really relies on the open chords John Fogerty used in it for it's signature sound. Change it to A and the color of the chords are now totally different.

It's really a toss up on changing the keys vs keeping the original key and groove. But if the singer can't sing in the original key, you really don't have too many options other than changing the key or the singer.

Perhaps another, better option is to choose your songs carefully from the list of songs that you CAN sing comfortably. Avoid the ones that are difficult due to the original key being out of range and the ones you're not willing to re-work into a different key.

The upside to changing keys is that it affords the opportunity for you to work up a totally unique version of the song since the original sound won't be a part of the feel.

You can find my music at:
www.herbhartley.com
Add nothing that adds nothing to the music.
You can make excuses or you can make progress but not both.

The magic you are looking for is in the work you are avoiding.