It sounds like the thing you don't like about miniatures is the mental perspective change caused by seeing (a figurine representing) your character "from the outside".
If so, my suggestion would be to replace the miniatures with something more abstract that serves the same practical function — providing a shared tactical view — while being deliberately abstract enough to avoid the loss-of-immersion effect. Basically, something that doesn't instinctively say "that's my character there" but simply "that's a map of where my character is."
There are several possible options that you could consider. For example, if you like the precision of a gridded battle map, you could keep it, but just replace the figurines themselves with abstract markers like, say, colored plastic / wooden blocks, unit markers from a strategy game, spare dice or just pieces of paper (or post-it notes) with character names written on them.
Alternatively, if you prefer a more free-form tactical representation, consider using a whiteboard and just sketching character positions and relevant environmental details on it, something like this:
Of course, you could just use a sheet of paper for this, but a whiteboard is more convenient, in that you can keep erasing and redrawing it as characters move about.
From a tactical / metagaming viewpoint, the nice thing about using a whiteboard like that is that you can include just as much or little detail as you like. For instance, if there's a hidden NPC in the bushes, and the PCs hear him moving about, you don't have to place an actual miniature in some specific position on the map to represent him (or leave him unrepresented) — instead, you can just write "rustling" in the general area of where the sound came from. (Of course, you could also do the same thing on a dry-erase grid mat, if you prefer.)
All of this is kind of the opposite of the usual trend in miniature gaming, where most people would prefer to have more detailed and realistic miniatures. But if you really feel that seeing your character from the outside hurts your immersion, this just might be a solution.