The Tzlach (Berachos 26a) asks on the Magen Avraham that one should be able to daven during the half hour after chatzos, mema nafshach. One should be able to daven then and have in mind that if it is not yet chatzos then his tefillah should be considered tefillas Shacharis. But if it is already after chatzos it should be considered a tefillas Minchah. Then after six and one half hours he should daven again, for if the first tefillah was tefillas Shacharis, now he is davening Minchah on time. And if the first tefillah was considered tefillas Minchah for it was already after chatzos, then the second tefillah that he is davening after six and one half hours should be considered tashlumin (a make up) for missing Shacharis.
However according to the opinion of the Rambam cited earlier, one may never daven Minchah before six and one half hours since the tamid shel bein ha’arbayim was never brought then. This question would only be applicable according to the opinions that one may daven Minchah from chatzos and on.