I am francophone as well. And to me, “je veux qu’il ait ouvert la porte” sounds right, if a bit stilted, provided we add an indication of time, while “je veux qu’il ait la porte ouverte” sounds like Yoda-speak. At the very least the verb is not well-chosen. I would accept “je veux qu’il garde la porte ouverte.” But the reason why we use the present subjunctive in this last sentence is that the action of the subordinate clause is concurrent with the action of the main clause.
OTOH, according to the page I linked to in my last post, when the action of the subordinate clause is anterior to the main clause, or posterior to it but anterior to another moment in time that’s being mentioned, the past subjunctive is called for. Does the example there, “je souhaite qu’elle ait fini demain,” sound incorrect to you? I don’t think it is, and it definitely has a different meaning from “je souhaite qu’elle finisse demain.”