Cheapest way to charge a 15V battery from solar panels?

update - I’ve found a relatively cheap DC-DC converter on eBay - 20A, variable output voltage:
…would this be the answer to my problems?

I have 400W of nominally 12V solar panels. At peak power they present around 17V.
The panels produce enough power for our nightly needs (30Ah/day), but storage is the problem: car batteries are horribly inefficient and waste a large proportion of the juice, so I’ve just bought a monster 60Ah Lithium battery (LiFeYPo) to store the power.

The problem: the new battery operates between 10 and 16V; if I use my existing 12V solar charge controller the battery is never charged beyond around 13.2V, which equates to around a quarter of its capacity.

What would be my simplest approach to charge this battery from the panels? I want to charge it up to 15V ideally.

I could:
a) connect the panels straight to the battery, via a blocking diode, and an over-voltage cut off (arduino + relay)
b) use an off the shelf (ie eBay) DC-DC buck converter set at 15V. I’m not clear on what impedance this would present to the panels though: if the battery is fairly flat it’ll happily absorb as much current as the converter can produce, but does that mean the converter will look to the panels as if it’s nearly a short-circuit? (If so, it won’t harm the panels, but they won’t operate at very good efficiency)
c) buy a simple (ie analog) PWM 12V controller and try and hack it to produce 15V instead … (I’m guessing that somewhere inside there’ll be a feedback resistor I can play with)
d) keep looking for a proper solar-lithium charger (specialty item = horribly expensive)
e) build a custom PWM controller for it (bit advanced for me, especially if it’s got to handle up to 30A of current)
f) stop complaining, stick with my MPPT 12V controller, live with the reduced capacity because it’s still working miles more efficiently than the lead acid batteries.

Thoughts? Budget is tighter than a gnat’s chuff, so hacky solutions are grand. Over- and under-voltage protection are trivial to implement (I can watch the voltage with an Arduino, cut things off with a relay in case of danger). The lithium battery is designed as a swap-in replacement for lead-acid batteries, so it’s fairly resilient to abuse (as opposed to vanilla Li-Ion cells). It can handle up to 60A of charge current, way more than I could ever produce.

(Gotta say, I love this lithium battery - stick 10Ah into it and you can get 9.9Ah out of it again, as compared with lead acid, where I’d be lucky to get just half the juice out again)

You need a maximum power point tracking charger that is designed for lithium charging really. I dont’ know
if they exist, but there probably are some fairly general purpose ones that can be configured.

You need to worry about protection circuitry when dealing with lithium batteries, overcharge and undercharge are both
dangerous situations leading to cell damage and safety issues.

Panels need to have about 40% more open-circuit voltage than the battery voltage otherwise they won’t provide enough
current - the max efficiency point is a significantly lower than the open-circuit voltage. Otherwise a boost-buck converter
is used (as in tracking chargers) to match the panel to battery.