No, that's a pretty reading, tbh.
Your thinking is at least along the lines that it needs to be while interpreting these.
One question you might ask yourself is whether Virgo is indeed not
your Ascendant sign.
Edgar Cayce, the famous American psychic/intuitive/astrologer from the early 1900s, posited that one's "soul birth" was not necessarily the same as one's "birth time" (i.e., what's on your birth certificate). He posited that a child's "soul" might actually be born up to 4 hours before their official birth time. If this is the case, then your rising sign could be different by one, two, even three signs over.
For a Virgo rising, that would mean Leo, then Cancer, and then Gemini.
You might want to check those Rising signs, and see if they fit better.
If one does, then you might want to also adjust all the other subsequent houses in your chart (i.e., adjust your birth time accordingly).