First off, let me say this is a very neat site! I have just wandered here yesterday and decided to sign up for an account as I have been looking for a place like this where we all as a collective can teach and learn from each other. I am excited to explore the site more.
I have had similar experiences to what you have noted above and your right it is hard to describe (as is most experiences in meditation...we don't really have the vocabulary to descrcibe the experience accurately) You have the correct insight and is good that you are able to realize with your rational mind that "there is nothing wrong with this". Also, Wndancer made some valid points, especially concerning the separation in the world and how we realize this to be the reality until the illusion begins to fade. I think the most helpful tip I could give you is something that you actually mentioned within your own post, " I guess I simply have to get more used to it." I think that when you are meditating and are getting to such a "deep place" you are loosing awareness of the borders/boundaries which can be a bit frightening...
You may wonder (as I did myself), why is it happening that I get the feeling of being scared if in my mind I know this is not a bad thing and I don't necessarily feel scared in the sense of what happens in my mind? We have to keep in perspective that the human body has been in a sense "trained" over thousand of years of evolution to operate in a certain way most conducive for our survival and as a result, our ego has also learned a certain way to operate within those boundaries through many past lives. through meditative practice you are changing your thought process and become more aware of the ego and becoming more detached from it. As you are entering the deeper meditative states your I awareness is beginning to fade and boundaries become seemless. That act will cause a sense of fear in the ego because it is like you are loosing yourself. [The ego is so darn strong! ;) but it has an important role]
I have a few other ideas about this, but I really want to refrain from speculation and throwing out too many opinions without understanding the situation. I think what is important to understand is that the fear you are experiencing is likely an illicited physical response that is more 'automated'. All that really means is you just need to keep at it because in a sense you are re-training your body/ego and interactions between two. Your starting to no longer operate from a 'survival mode' which is when is one is operating from the ego. Just keep practicing!
It is also helpful to remember and remind yourself: there is nothing to fear.
I hope the way I wrote that wasn't too confusing, I may have jumped around a bit, but maybe something in there will be helpful.
Thanks for sharing your story and creating this site!