The dimensions I observe...while those verbs used...
I think this might be the problem. Extra dimensions and so on are in aid of predictions made by mathematics. They are irrelevant to the imagery of 3 dimensions, and they cannot be explained using the language of verbs. The reason that these ideas "do not combine to make any sense" to you is that you are combining crude metaphors for the concepts in question. You are confusing a set of very rough maps with the territories they unsuccessfully try to represent.
Mark Twain covers this sort of error very well in Tom Sawyer Abroad, where he has Tom and Huck arguing whether the balloon in which they are riding is over Illinois or Indiana based on the color of the ground not matching the color of the states as found in their school atlas.
Our brains simply cannot make sense of this field using mental imagery that was evolved from our ancestors' very limited ability to observe the universe.
Do you leave out the possibility that the same reconciliation of the two sets of equations might be achieved by some other, more simple and elegant means without invoking any redundant entities?
Of course not. It simply remains for you to do the work of formulating such means. Until that happy day, your inability to fit reality into a metaphor with which you are comfortable remains an issue of semantics, not of physics or mathematics.