It is now a LAW that under 4'9" or 8 years old, they have to be in a booster seat, so you don't have a choice in the matter, other than which booster you'd prefer in place of your convertible. They are less expensive than the convertible seats (we have 2 convertibles also), and the boosters are SOOO much easier than the 5-pt harnesses, though I was uneasy about taking my son out of his 5-pt. But everything has been fine. Also, she is not yet tall enough for a backless booster, so you'll need a belt-positioning one. Whether it converts to backless or not is really not a big deal, just a personal preference if you choose.
Are you sure you're routing the seatbelt properly in the seat? I don't have that seat, but have read numerous reviews which gave it outstanding ratings, so I'm surprised to hear someone unhappy with it... You may need to raise/lower the back so the shoulder harness lays properly??? Just thinking "outloud" if you will, LOL.
We have a Graco Turbo with the memory foad padded seat. My son seems to love it, though in the summer he does mention his back sweating. Also, if you do any lengthy traveling, I have to say that their little heads bob around when they fall asleep, even with the side "wings." My son looked so much more comfy sleeping in his convertible, than in his booster. If have a van, or any vehicle where the actual seat of the car will recline, then the booster will recline slightly with it. The rear seat of our SUV won't recline, so we don't have that option. Also, Evenflo makes a nearly identical version of the turbo that has little lights on the "wings" they can click on to read a book or what not when it's dark. I wish I'd have seen that one first... But we do love our Graco... Good luck...