The Powermax converters sold on Amazon have a 14.4v Absorption voltage.
The Powermax converters sold through bestconverter.com have 14.6 ABSV
Trojan's want 14.8v remember. This is not just a 'close enough' sort of deal. Adequate Time at absorption voltage is the recipe for happy long lived batteries. Inadequate time and not meeting the manufacturer recommended ABSV will have a person whining and complaining and freaking out when their batteries 'no longer take a charge' prematurely.
No matter how good Trojan T-105's might be, they are not immune to user error, and not meeting the recommended 14.8 ABSV is simply user error.
Best converter sells a manual, adjustable voltage Powermax converter. Not automatic! The user can choose any voltage between 12v and 15.5v, and the batteries themselves decide how much amperage they want at the chosen voltage, up to the converter's maximum amperage output. The use of such a device requires a human with a brain, as holding batteries at ABSV longer than needed is abusive to the battery. Holding the correct ABSV for as long as needed and no longer is the holy grail of lead acid battery charging, and very few, if any, automatic battery chargers get it right, no matter how well marketed they are.
A good turkey baster style temperature compensated Hydrometer will prove this. This is the best flooded battery tool available. Without it, one is guessing at various clues. When one expects to see specific gravity at 1.275 or higher, and finds the green light blinks when the batteries are at 1.225, only then does one realize that their charging sources are NOT completing the task of fully charging a lead acid battery, which is so vitally important for their lifespan.
My current flooded battery, 2 weeks after purchase, was down at 1.210 after 13 cycles and recharging at 14.7absv for 2+ hours and floating at 13.2 the rest of the day. Long story short I had to bump this upto 14.9v and then push float voltage upto 15.3v for the rest of the day, and only this solar regimen along with at least a 16v 2 hour long EQ cycle monthly, allowed this petulant battery to live through 350 deep cycles at this point.
Had I believed various blinking green lights, this battery would have been violently slung though USbattery's office doors with a hate note attached on day 30, when all along it was inadequate voltage and time at Absorption voltage that was lacking, and the Hydrometer was the only tool which made this realization possible.
A problem with the charge algorithm of Powermax, is once the battery rises to and reaches ABSV, then it drops the voltage to 13.8v and thus the charging amps dwindle to the insignificant level. No big deal if one has a week left to plug in and complete the recharge, but it is a big deal if one wants to be sure the batteries are indeed fully charged by the next morning.
An Iota( with a 14.8 ABSV), would be a better mate for Trojan batteries, and yes, absolutely, have a capable charging source/powersupply available for when you plug in. Performing an EQ cycle on the batteries when needed will greatly extend their lifespan, and often grid power is needed to accomplish this task, if only to power other devices when one has enough sunlight to set the solar voltages up into the mid to high 15's for an hour or 2 or 4.
Solar is great, but I think that you are vastly overestimating its Harvest . With the panels flat on the roof, on a cool and cloudless June 21, only expect 95% of the panel rating for 1.5 hours on each side of noon. Lots of amp tapering before and after that sweet spot. I get a feeling lots of your calculations are for maximum wattage all daylight long, when it is rarely possible to even make the rated panel wattage.
I took a HD 12 awg extension cord, and fed it through my firewall, and mounted it so the 3 prongs are accessed by a little hinged hatch below my driver's side headlamp. Sometimes at night, I need a little light to plug in, usually though I can do it by feel. With it located here, it is a bit less noticeable, and I can run the cord under the van and around a tire, and 90% of people will never notice it.
Feeding an extension cord through that device in your first post will get old quick.
Running an electric cord through the door seal or window also gets old quick.
Worry about the cord's insulation being crushed and degraded by being stepped on and closed in the door. So many household fires are started by abused extension cords.
While I have a 120vac adapter for my laptop, which is my biggest electrical consumer, when I have AC power available, I just let my 41 amp power supply hold the batteries at the voltage I choose, and it powers all my 12v devices. This would slow down battery charging as ~ 6 amps that could be going into lead acid batteries, are now going into the laptop. Rarely a factor as time to full charge is rarely a concern when grid power is available, for me.
I bought a 12v only fridge, instead of an AC/DC, not only because it was 100$ cheaper, but because 110$ got me my 41 amp power supply which can power the fridge from grid power, and capably charge any lead acid battery I ever choose to employ. The AD/DC fridges basically have a small power supply inside them for voltage conversion. So I figured why have 2 devices doing the same task. No regrets.
If you are still planning on running air conditioning for more than 30 minutes, you will need a generator.