I'd have replied sooner but I've been out all day and you didn't send beer money, so...


Both gate drivers look fine. Pick the cheaper one, I suppose. (I've got a TPS28225 in a recent project, which seems to be doing fine.)
ATtiny85 is not fast enough to control current. You need more like a 10MSps ADC to do that at this Fsw. Use a purpose-made regulator or controller IC instead. Get one that controls output current internally. Vary output voltage by tweaking the feedback node with a DAC to a resistor to FB. (DAC can be PWM, in which case split the resistor in half and put a nice big filter cap in the middle.)
Might as well implement temperature and UVLO in analog as well -- a dual op-amp or comparator takes up as much space as the ATtiny, though admittedly the resistors supporting them will take much more space, of course. (A few years ago, I designed an all-analog circuit of similar capability, with a boost power stage to run from a single cell at up to 10W.
https://www.seventransistorlabs.com/Images/Flashlight2Sch.png https://www.seventransistorlabs.com/Images/Flashlight2_Schematic.png ) Only reason I see to bring out a MCU is if you're more fluent with it, or if you wish to add complex functionality like selectable blinking.
Don't see a need for absurdly low Rds(on) -- that really invites more problems (switching loss, short circuit / fault / shoot-thru current) than it fixes. Optimize between switching frequency and Rds(on).
Could maybe go for a two-phase interleaved design as well, but eh, not really a problem here. The advantage is easier switching -- each inverter switches half the current -- and less input and output ripple current, offering some savings on filter caps. If you are optimizing for size, hmm, not sure which one is better, you'd have to try both.
If you want to run super fast, you may consider a resonant design as well. Kind of stupid for a non-isolated LV converter, but it could go at a few MHz, and you might consider GaN transistors as well (which would go with a similar gate driver, but designed for Vgs(on)=5V, and higher dV/dt). The problem then becomes, there aren't really any controllers yet that go that fast, they all top out at 1-2MHz or are integrated (regulators instead of controllers), so you pretty much have to roll your own. (Which isn't all that painful: the core is a gated VCO. Adjust frequency to control power over a modest range, then cut it off completely (hysteretic mode control) to cover the low range.)
Keep in mind that you'll have a lot of reactive power in the filter inductor (5-30 VA, same or greater for resonant), so it needs a high Q (20-100+?) to not trash your efficiency budget. It can be hard to find inductors rated for Q at frequency.

Lots of shopping around.
I don't see much reason to optimize for efficiency -- you're burning ~20W of heat regardless, and another one or even two watts will make no appreciable difference in heat dissipation or run time. Don't sweat it.

Tim