I would not encourage anyone to spend above their comfort level. That said, I think you may be over estimating the expenditure of time, money and knowledge needed for a 12V compressor cooler setup.
Solar is not required. I have a mid sized system that powers a fridge, induction cooktop, and convection microwave. Given vehicular and shore recharging options, solar is not worth the increased complexity, lost aesthetics, and reqired roof space to me.
The simplest 12V setup requires only two components: power station and cooler. 12V compressor coolers can be bought on Amazon for less than $200. A power station capable of running it for 24+ hours can cost less than $250*. These coolers are insulated, so it can take hours (depending on ambient conditions) for the temperature to drop significantly in the absence of power. These coolers also have a drain plug, so ice can be put in it to extend the time even further.
I have a 60L Bodega, typically set at 35F, it could take 12+ hours for it to rise 20 degrees when the ambient temperature is 75F. I’ve inadvertently tested this a few times, discovering my cooler was off because my power station shut down**.
Option 1 you mentioned sounds like a thermoelectric cooler. A few years ago, compressor coolers were $500+. Unwilling to spend that much money, I bought a thermoelectric cooler for $125. They have a limited ability to cool (or heat), capable of maintaining a temperature of only 30-40F below ambient. In addition, it requires constant power (it doesn’t cycle) so the power consumption is greater than compressor coolers. I was dissatisfied with mine. Even when driving, it was unable to keep drinks refreshingly cold. I didn’t have a power station, so when parked (and therefore unplugged from the car) drinks quickly went from moderately chilled to icky tasting warm. Needless to say, using it to keep food was unsafe. At todays prices, there is no reason to buy a thermoelectric cooler.
I don’t understand the appeal of option 2. I have no experience with high quality ice chests like Yeti. Since they cost as much as compressor coolers, I will likely never use one. I’d love to play around with the uber portable battery powered compressor coolers like LiON. But it's not very cost effective, yet...
You inquired about a 3rd option. If money is really tight, consider buying a compressor cooler and power it via the cigarette port when driving and ice in the absence of power. You will probably discover that you need ice less frequently than you think. You will probably discover that you need a power station sooner than you think.
I did not realize how useful having portable electricity is. Apart from its use in the van, I’ve used it for powering tools, vacuums, electronics on the beach, in the park, at the laundromat. I use it in the house and in the yard instead of running an extension cord. Even if/when I have a permanently installed electrical system in the van, I will always have a power station. Now that I’m used to the utility and flexibility it affords, there’s no going back.
Here’s an article comparing the 3 types of coolers.
https://www.readysetoffroad.com/cooler-thermoelectric-cooler-12v-fridge-freezer-which-one-is-best/
* Amazon has a $50 off sale on one of the best small power stations on the market right now, the newly released Bluetti EB3A. Here’s a review and Amazon’s link.
https://www.amazon.com/BLUETTI-Portable-Recharge-Generator-Optional/dp/B09WW3CTF4/ref=sr_1_3?crid=3MX6J8YR4N7RE&keywords=BLUETTI+EB3A&qid=1656709903&sprefix=bluetti+eb3a,aps,94&sr=8-3
** EcoFlow power stations are known to shut down if there’s no draw for a period of time (I think its 15 or 30 minutes). Fridges only uses power when the compressor is running and the frequency of cycling is a function of the ambient and set temperatures. At sub 80F ambient with thermostat set to 30 something, it may not cycle enough to keep the power station on. My solution is to lower the thermostat (under 32F) such that it triggers the power station frequently enough to keep it on.