DC-DC converter for input voltage lower and higher than output voltage

Hi

I need a CCCV dc-dc converter to bulk charge a lead-acid battery in my boat at 13.8v from a 4s (16.8v) pack. But I'm a bit uncertain on which converter I should get. 2-5A would be sufficient.

I thought about getting a LM2596 cc/cv but it's a step down converter, but my input voltage is at 16.8v at peak and lowest 11volts, which means I would cross the voltage area where it's not a step down converter but would need to boost voltage by 2,8volts at minimum voltage from the source.

Any suggestions? Cheers

Why not just use a real charger like the IMaxB6 that takes DC input between 11-20v and output controlled charge for various pb cell configurations ?
Lots of similar RC charger options under $40
https://www.ebay.com.au/itm/iMAX-B6-80W-6A-Digital-RC-Battery-Balance-Charger-Discharger-NiMh-Li-ion-Ni-Cd/263289024061?hash=item3d4d3fae3d:g:iR8AAOSwb3laKJ-L

That's a really good idea! Thanks! This gives a lot more flexibility too, with chargeprofiles.