It's important to note that breastfeeding research and advice in general has moved on since Tracy wrote her books. If she was still with us today we like to think that she would have updated her books to reflect this. It is well established that breastfed babies at four months need one, two or even three feeds overnight so I personally wouldn't actively think about weaning night feeds unless they were excessive or once solids are fully established at 7-8 months+.
If she refuses the catnap can you bring bedtime earlier so she doesn't go to sleep overtired? Or can you get the nap in the car/stroller so she doesn't refuse it?
I do think that a cut in her daytime sleep is probably needed, or a longer day, so pushing her routine on a little should help. She may be more willing to take a catnap if you offer it later closer to 6 instead of 5.30 (1h45 is on the short side after a mammoth 2.5h nap) and that will give you a longer day.