The idea (which I'd like to test, first at low power) is to use the synchronous PWM stage as a kind of DC "transformer" where the PWM duty cycle sets the "turns ratio" in front of the battery. It's synchronous so never in DCM where large duty cycle changes would be needed. The duty cycle would then be changed as a function of the measured sodium-ion battery voltage (filtered, no need to respond very quickly), so it roughly matches lead-acid at the other end.
Almost full cell at 3.75V multiplied by step-up gain of 8 is 30.0V at the charger/load end.
Almost empty cell at 1.8V multiplied by step-up gain of 11 is 19.8V at the charger/load end.
For intermediate cell voltages, set intermediate gain: Gain(Vbat) = 8.0+(3.75-Vbat)/0.65
Outside the range, keep gain constant at 8 or 11 for a while, then cut off charge/discharge if out of safe range.
No need for complex control loops, just a fast overcurrent limit for protection (hiccup mode - turn off all switches in hardware then soft-start in software again) above working range and below inductor saturation. The charger and the load are already current-limited. I wouldn't recommend doing this with Li-ion or LFP as these need very accurate voltage control (that may be the reason why no one is doing it that way, and no one makes suitable controller chips), but Na-ion has a wide range (1.5 to 3.95V are the limits, 1.8 to 3.75V is well within with only small capacity loss) and charges almost linearly (like a big capacitor).
My bigger plan (if the small one is successful) is the already mentioned 24S Na-ion pack to 48V inverter matching device. I don't intend to replace the BMS/balancer - a 24S JK BMS with custom settings modified from LFP should work. Almost full at 3.75*24=90V, gain 0.64, 57.6V at the inverter. Almost empty at 1.8*24=43.2V, gain 1.0 (minus some losses), 43.2V at the inverter, the function in between matched so that the inverter shows reasonably close SOC as if there was a lead-acid battery (there might even be one in parallel, if matched well enough). About 3 kW max total power split in 3-4 phases. For better efficiency (light load most of the time) switching frequency could be changed to mostly avoid hard-switching, and disable some phases at light load.
Quite a lot of work, and it might be a waste (except the CV factor) if in a year or two China starts making millions of such converters, dime a dozen. More likely though that sodium-ion batteries will need new special inverters (with a wide-range DC/DC converter between the battery and the HV bus), instead of using the existing ones.