The problem you may run into is that you won't know what the voltage is where you are plugging into ahead of time. If it's low where you plug in, it will be lower inside your TT (amount depending on wire gauge, length and current draw). If a receptacle looks questionable, I'd even consider finding another one nearby if possible. Plugging into a completely unknown source can carry more risk, especially when "around the back" of a building and it's not normally used for RVs. See "No Shock Zone" info. below. I would only use a dogbone style adapter at the end of our cord in case it ever overheated. That way, you'd hopefully only lose the adapter.
I would go for the two #10 extension cords. Available online for about $50-60. Having two x 50' cords is a good compromise and will give you a spare for when you may be in a campground and your 25' shore power cord isn't long enough. Always keep your cords lengths to the minimum possible.
You won't be able to run much additional on a 20 amp circuit when the AC is running. If the voltage drops, an AC unit will draw more current and can cause a breaker to trip. If that happens, suspect low voltage as the cause.
As above, get and use a voltmeter when you plug into a new location and monitor it in case it drops. I would get a plug in digital multi-meter (cheap at HF) as it will allow you to check a receptacle before plugging in (L-N, L-G & N-G). It's good that you have a "surge protector" as that will protect you against low voltage automatically. If you don't have a readout display for your EMS, a plugin voltage monitor may help.
When plugging into unknown receptacles, there's always the risk of an improperly wired receptacle. I don't what to make things seem complicated, but there is some info. here at
No Shock Zone - hot skin and
No Shock Zone - "little shocks". You may want to get a non-contact voltage tester. There is also some info. on RV extension cords on the same website:
RV cordsAlways turn the power off before plugging into a receptacle. Easy to do at a campground, but at the schools, you'll need to shut off the main 30 amp breaker in your converter panel. If you don't, the inrush current of the converter will cause pitting on the metal blades of plugs and inside receptacles ("connectors" at end of a cord). Pitting will eventually lead to overheating of the metal contacts which causes an eventual meltdown. Ensure that your plug blades are always kept clean. Plugging multiple cords together increases the possibility of more resistance from the connections.