L’maaseh, the sefarim I’ve been looking at seem to say that al hamichya either exempts the rice or it’s a safek if it exempts the rice. This would mean that you definitely should not be eating it without a new bracha, and perhaps you shouldn’t be eating it at all (unless you find someone to be motzi you).
In Rav Bodner’s Hilchos Brachos sefer, he quotes the Shaarei Teshuva that if you ate regular mezonos and rice and said al hamichya, the al hamichya exempts the rice and you are no longer allowed to say a borei nefashos. (which would also imply that you shouldn’t eat more w/o a bracha).
He quotes the Ben Ish Chai that you are supposed to say just an al hamichya l’chatchila, and the מגיה לחסד אלפים that you should first say a borei nefashos and then an al hamichya. It sounds like according to the “magiah l’chesed alafim”, it must be a safeik whether or not the al hamichya exempts the rice, whether or not you want it to.
Based on these sources, it would seem that it’s a safeik and the best thing to do would be to not eat the rice.