Your presentation reveals an absence of a required distinction to resolve the trap you have constructed for yourself. To paraphrase, you are excellent at getting people to like you; you perceive that you have to pay a price for achieving such a relationship with people - specifically, you may not be yourself (whoever that may be - hell, maybe you're the guy who doesn't act himself to achieve being liked).
Somewhat more seriously - the required missing element is the distinction between process and content. Your identity, insofar as it exists is a content issue - who you are..., while nlp with its unflinching committment (in some quarters) to process focuses cleanly on a sequence of subtlely replicated mirroring (or lateralized mirroring) procedure. See pages 281 - 282 in Whispering for a description.
These processes allow the user to achieve the deep rapport (unmerited, of course) relationship of utility without changing any aspect of the presentation of self (other than following subtlely the non-verbal aspects of their companion's behavior. Thus, no compromise is required. But these are mere words floating on the monitor in front of you until you muster the effort to actually go out in the world and play with the strategy detailed in Whispering so as to make it a smoothly functioning portion of your repetroire.
It's one of the those relatively rare having your cake and eating it too.
All the best,