Ok, very tempted to help you. My bucket list is endless but this is for sure on it and also an inverter coupled to an EV.
Be aware of the safety risks involved, anyone that once experimented with 2 solar panels in series to make some nice arcs knows what I'm talking about. An EV battery has a lot more potential...
So how far are you with the idea? I like the buck/boost suggestion, do you need galvanic isolation? Nowadays there are little gti's with galvanic isolation either and galvanic isolation is not necessarily more safer. Since you have 3 strings I would aim for 3 modules of 5kW that can work in parallel, it won't hold you back to build them in the same enclosure.
Sic mosfets are nice but still expensive and used in this kind of applications were we work with high frequencies, although the price difference with IGBT's is getting smaller I would start with igbt's and work with a frequency of 20-50khz (on the edge to use igbt's). You might want to start with a "proof of concept" before going for higher efficiency. Also, higher frequencies will need a more careful pcb layout.
Are there things you already have laying around, because this can quickly get very expensive to source semiconductors, inductors (sendust, ferite, iron powder cores,..) capacitors, lems,... Broken gti's could be a good starting point, but it is advisable to use new semiconductors...
Allthough it is wisely to start with something like 48V to get a certain feeling, it surely is another world once you get in that 400V range. The buck and boost inductors need to be calculated for your working point, unless you start playing with the frequency. If you build in a current limit, you can start experimenting on low power levels.
Is there a place were I can get more information about "how to acces the battery itself"? I supose there is a a relay and other stuff before you can realy acces the potential of the battery and is there a difference between drawing current or pushing current?