Firstly, you were correct to put the mezuzah up since the halachah follows the opinion cited by the Kitzur that doorways are obligated even when they lack doors. According to some commentaries, even the Kitzur would agree in a case where you can’t put the doors up immediately.
Nevertheless, now that the doors are installed, it would be correct to take them off and reattach them to fulfill the halachic requirement of actively affixing the mezuzah and not relying on one that was affixed already.
You would not need to make a new berachah then as the original berachah you made when first putting up your mezuzot is still in effect. In fact, many authorities rule that this is true even if you hadn’t made any berachah at the time of putting up your mezuzot.
 Shach, Y.D. 286:25. Chayei Adam 15:9; Misgeres HaShulchan 11:10.
 Chayei Adam 15:9; Mezuzot Beitecha (286:22) requires this even in a rental property.
 Chayei Adam 15:9; Aruch HaShulchan 286:24; Hagahos R. Akiva Eiger to Shach 286:25; Chovas HaDar 10:4:6; Cf. the sources cited in Sha’arei HaMezuzah (11:43:94) that allow reciting a berachah in some cases.