About this:
------ I've also seen that I can order the combo ticket online and make the reservation now, but I would have to pay for it separately from the Firenze Card.
I just looked at the Firenza card site and says you must make the Duomo climb reservation at the Ticket Office (across from the Baptistery). I did not see any information reporting you can make a climb reservation on-line. I could not quickly find an official website for the Duomo. Was that a commercial vendor or tour?
How long will you be in Florence? If for more than 3 full days, It might be worth your money to buy the Firenza card and the separate Duomo pass and visit the Duomo sites before or after the 72 hours you will spend on the other sites covered by the Firenza card. If not, good luck choosing what to do in those 72 hours! The climb is definitely worth it. I suggest an early morning climb: it will be less crowed at the top.
If you miss an opportunity to climb the Duomo, do consider a climb up the tower. You will get a close-up look at the outside of the cathedral as well as spectacular views of the city.
Also, do go to the official Firenza Card site, click on the Learn More button then click on the Watch It button. You will not get to a video, but to a chart of all the hours of operations opening times of the sites covered by the card, including any special closing times during June (you will have to look at this closer to June). This will be useful in scheduling your time.
I was just in Florence at the end of March. Feel free to PM me if you have any questions...while my visit is fresh in my mind.