Pro: Excellent song list!
I definitely undertand what you are saying. All your listed tunes are indeed recognizably popular standards but thankfully not the worn out overplayed songs ones which have reached the overexposure level as BEG.
I include some of the same songs in your list in my repetoire too. The KEY is to find good quality songs which are still recognizable (but not necessarily the biggest hits) , yet interesting enough(melodically, harmonically and/or rhythmically) to give us the opportunity to present something of ourself creatively to the song.
If I do an Elvis or Sinatra tune, I avoid songs like 'Love Me Tender' and 'My Way', which have attained karaoke parody fame, but instead (like you) look for those more 'off the beaten path' songs which are still recognizable and more easily allow you to present your own rendition. In contrast, I've found that audiences expect you to do 'My Way' & 'Love Me Tender' just the way Sinatra & Elvis did it. I'll leave these songs to the Elvis impersonators.