I'm looking forward to seeing you is correct.
until is most often a conjunction. That's how it's used in
until you arrive.
When used as a preposition,
until usually takes a noun object, not a gerund, as in
until sunset, until the end of the year, etc. In the case of your example sentence, the noun form of
arrive is more commonly used than the gerund:
Until your arrival, I'll clean the house.
When a verb is used as the object of the preposition, it has to be in
gerund form. You are right about that. But if the subject
of that verb is missing, then it is taken to be the same as some noun
in the clause it modifies. So
Until arriving, I'll clean the house means
Until I arrive, I'll clean the house (which makes no sense).
Until arriving, I'll clean the house cannot mean
Until you arrive, I'll clean the house.
Even though there may be a few cases where
until is followed by a gerund, it's not usually very idiomatic.
CJ