MOSFET driver for digitally controlled, battery powered boost converter
I think you've covered most options, though one I can think of that you didn't list explicitly is making a charge pump manually. It isn't infeasible since you have a microcontroller. If you have access to cheap passives, that could be cheaper than a charge pump IC.

However, the cheapest, smallest, and most efficient option is probably going to be the integrated solution. It's also simpler and going to have a better chance of working properly under all conditions. Semiconductor companies make big bucks creating switching regulator controllers which are cheaper and smaller than you could create them manually. That said, there is something to be said for the additional control that comes from doing it yourself.

But, I can't think of and I don't know about every other potential solution, so just for fun, let's explore the Rube Goldberg machine and see if it really is too complicated.

Here is a quick simulation I threw together of the complete circuit:


Here's the bootstrap and output voltages (note the 100mA load above):


Here's the gate drive waveform (100 KHz) once it stabilizes:


LTSpice reports the following average powers:


Q2: 11.478mW (9W peaks)
Q3: 17.457mW (2.7W peaks)
M1: 26mW (60W peaks at the beginning, ~10W peaks once stable)
D5: 4.74mW (60mW peaks once stable)
V1-V4: 71.931mW + 1.448W + 70.483mW + 1.6649mW average
R5: 1.152W average, giving us 72.3% average efficiency over 40ms.


Up in the top-left corner we have our bootstrap voltage creator (Dickson charge pump). It's not the best design, but in simulation it gives you 9-12V at a low voltage from two GPIOs (V1 and V3) on your microcontroller PWMming opposite of each other. LTSpice says the average current of V1 and V3 is 1.3mA, but the peak lives around 120mA. I'm sure you could tweak it to be much stronger (use one of those non-inverting gate driver ICs as a buffer for the 0-3V signal into the capacitors). In terms of components, the schottky diodes often come in packages of two, so that's two and a half SOT-23's and five MLCC caps. Alternately, you could just use the charge pump IC instead of all this.

Near the middle we have our totem-pole (aka emitter-follower) gate driver and simple level shifter. Someone once told me that gate drivers are like putting boxes within boxes. You start with a small box (power and voltage capability), put that box into a larger box, and so on until you reach the required drive strength and voltage levels. The totem pole (Q2 and Q3) should be eerily similar to the ZXGD3009DY you mentioned in option 2 and can be replaced with a single IC. The level shifter (Q1, Q4, R1-R4) is a very simple, unbalanced (the low-level impedance is quite a bit higher than the high-level impedance...but that totem pole doesn't mind too much) arrangement which works well enough in this situation. If needed, you could put the level shifter into a high-impedance 12V buffer and feed that output into the gate driver to balance things out and provide faster switching times.

Alternately, I might suggest something like the MCP1406 instead of the discrete gate driver, as it integrates level shifting and should work with 3V logic (2.4V min Vih, 0.8V max Vil).

Everything else is the boost circuit (M1, L1, D6, C6) and the microcontroller (all the V's except V2).

In total, you would need the following components (aside from the boost converter parts):


3x dual-diodes, 5x MLCC 10uF caps (or 1 charge pump IC).
1x NPN and 1x matching PNP (or 1 emitter-follower IC).
1x NPN, 1x PNP, and 4x resistors.


That's 8-14 fairly small components and I wouldn't consider that too intimidating or Rube Goldberg-like. The fully integrated solution has basically all of those components inside of it (except the caps) plus feedback logic and such.

Really I think the only question is whether or not you need the control of a discrete circuit or the efficiency and small form factor of a fully integrated solution.