Besides the core, what other components do you have as this will have influence on your design? I am thinking of half bridge or full bridge driver IC's , voltage/current rating of mosfets, IGBTs, rectifiers, small cores (for pulse/driver transformers), etc.
You will need some form of power tracking (for example input voltage controlled maximum charge current). When, for example, the batteries accept 6A charging current, but the solar panel is not able to provide the power, the DC input voltage will collapse.
I would go for an isolated converter. From a safety point of view, you may expect several kV overvoltage transients because of the long vertical run and the system is partly outdoor (on the roof). Besides this, you should think about what happens when you get a full lightning strike on the roof or panel.
Without component limitations, I would go for a full bridge design with mosfets, as this doesn't require low leakage inductance and ripple current is relatively low. To reduce switching loss, you may consider zero voltage switching. If you can't get sufficient current control range, you could use burst mode control to get almost zero output current.
If you are familiar with phase shift between left and right half bridge, you can use that to increase the control range without losing zero voltage switching.
If you have very limited hardware, and are well into electronics and magnetics, you may consider a self oscillating solution in combination with burst mode control.