Any problems with double step-down conversion?
Why are you so stuck on using a PMIC that is not a good fit for your application?

There are a plethora of various types of PMIC parts available from multiple vendors. TI has parts with multiple DC-DC converters on board that can support 2, 3, 4 or more voltage outputs that are programable via precision feedback resistors.

Whilst it may seem convenient to use a part with lots of DC-DC converters in one package I find it better from a board layout standpoint to use PMICs with two channels and then use multiple chips if additional voltage rails are needed. It is just too hard to get an optimum layout trying to cram all the inductors, resistors and capacitors around a PMIC with more than two channels.