I remember "my" Cubase 5 VST for Mac (OS 8.6-9.2.2) could bounce in the manner the OP is looking for. It is a very handy feature to 'test' if a something 'works' in a song. And though sonically identical, listening to a bounce in iTunes is different from listening to the Logic project playing. So I understand the wish for it.
What I would do if I wanted to achieve this, is simply first do a
Save and then *Save as...* (don't include assets). I'ld call it something obvious, like "Mysongsoriginaltitle"-short version. My main project will stay safe, saved and unaffected, this newly saved version will be edited, as you recommended! So I'ld cut away the skipped section, Save +"Mysongsoriginaltitle"-short version,+ bounce +"Mysongsoriginaltitle"-short version,+ listen to +"Mysongsoriginaltitle"-short version+ in iTunes, say "Nēh, doesn't work" and trash the bounced file and the new project file. Or I'ld say "That's it!" and also cut the skipped section out of the
main project and continue finishing my very serious piece!
Message was de-embarrassed by: Eriksimon