I turn down invitations by females (repeatedly by the same female, currently, though in the past it have been different females) which may or may not indicate romantic interest - invitations to the cinema, to their place, for studying, etc.. I refuse to hand out my cell phone number, I don't answer e-mails, I consciously avoid eye contact and try to get out of conversations quickly.

Er... Why? Things usually described as creepy involve wanting to interact with someone regardless of whether they want to interact with you; if it's them who initiated the interaction (and so you know they want to interact with you), why would they be creeped out when you reciprocate? (Unless you have a reason to believe that the invitation was only for politeness' sake but didn't expect you to actually accept, that is.)