Ulizitupa, no. A verb can only have one object prefix. In this case, it's -tu-. If you add -zi- there, the verb can no longer be interpreted as -pa but must be -tupa (throw) ... so your sentence means "You threw the gifts last year."
Your logic is correct, but there are only eight verbs that retain the infinitive, of which two are not even monosyllabic. And 'Kupa' is not one of them. These verbs are: 'Ku-fa', 'Ku-ja', 'Ku-la', 'Ku-nywa', 'Ku-wa', Ku-wa na', Kw-enda', 'Kw-isha'.