I think you've figured out exactly what is going on. Of course she prefers the fast bottle, it's less work!
If it were me, I'd elimate the bottles or at the very least switch back to a slow nipple. But I'm a SAHM and it's my job to breastfeed, kwim? You can also choose to express your milk and feed her that way. You have to decide what you want, what she would be best off doing, and what works for your family.
You are so close to starting solids and eliminating milk feeds. The second 6 months go so fast! It's always nice to hear the moms who say, "gee, I just want to keep nursing" and pretty soon baby is 1 yr old! :wink: