The relevant Latin prefixes are sub- and super-, the first of which becomes sup- before a p.
Thus the analogous Latin verb would be superportare.
This verb seems not to exist in classical Latin, but there are a number of verbs prefixed with super-, so it is certainly a valid derivation.
The analogous English word would then be 'superport', if borrowed directly from Latin.
Many English words that came from Latin did so through intermediate languages, but I see no reason to take a neologism artificially through other languages.
Having said that, I must add that prefixed verbs in Latin often acquire a figurative meaning where the prefix cannot be analyzed as a mere indicator of direction.
Even in classical Latin, supportare does not seem to have sup- meaning "under" at all.
This is much like phrasal verbs in English; the preposition and the verb together form a fixed expression which has a meaning surprisingly independent of its constituents.
Moreover, if supportare had a literal meaning sub+portare, it would be "to carry under", not "to carry from under".
Carrying above oneself should be superportare, but there is no such word in classical Latin.
Prefixes can work in different ways, and it doesn't always make much sense.
It is best to treat prefixed verbs like English phrasal verbs: the prefix can inform a good guess, but it is not to be trusted.
The verb superportare does exist in medieval Latin, and it has no directional meaning one might expect with super- or supra-.
Mediae Latinitatis Lexicon Minus (I have institutional access) says:
> transférer des biens-fonds — to convey property — Besitz übertragen, auftragen.
I think it is pretty safe to say that supportare does not mean "to carry from below" but just "to carry".
The sup- has no directional meaning.
Therefore I would say that a substructure supports and a superstructure supports.