There has been a lot of good information shared here, especially by Lawrence Wade (from my perspective). But we're slightly left hanging about the two closely-related fundamental questions from the OP:
Will higher octane fuel, increase power while towing?
Will higher octane fuel impact the available power in common v-6 regular gas burning engine?
Strictly speaking, no, higher octane fuel will not increase power while towing, compared to "regular" octane levels.
Secondly, if we assume the engine is operating as intended, in good tune, and not overheating, no, higher octane fuel will not impact available power in a normally-aspirated engine such as your Honda V6.
That's not to say that premium high-octane fuel isn't recommended. Since loss of power and possible mechanical damage may occur if the engine isn't running within spec, high octane fuel is cheap insurance to make sure that the adverse operating conditions - like a heavy towing load, and climbing mountains - don't lead to pre-ignition or detonation.
The answers here have already established that pre-ignition and detonation are bad for your engine, and why, and the aggravating factors that can lead to those states. (They're distinct conditions, but not mutually-exclusive ones.) But as long as those conditions are not happening, then premium fuel will do nothing for you.
This relates to how your other two example answers from the question about economy are not in fact opposite responses - they're both correct, with importantly nuanced differences.
For most vehicles, higher octane fuel may improve performance and gas mileage and reduce carbon dioxide (CO2) emissions by a few percent during severe duty operation, such as towing a trailer or carrying heavy loads, especially in hot weather. However, under normal driving conditions, you may get little to no benefit.
This is correct because the author is describing conditions that push the operating parameters of your engine toward the edges of its envelope, and a little pre-ignition may occur as you're hauling that trailer up Pike's Peak. Having high-octane fuel will preserve your power output (such as it is - high altitude will still have reduced it a lot) by preventing pre-ignition. Thus, it may "improve performance" compared to regular gas if you usually lose power and performance while using regular gas.
But it doesn't inherently add energy or power over regular fuel. And as they say, under normal driving conditions, there's pretty much no benefit of any kind. I take this to simultaneously imply that the engine fuel mapping and ignition (and general state of "tune") is all well within normal limits.
One secret to lowering your overall fuel cost is to just use regular gas, unless your owner’s manual specifies a higher octane gas. Most RV's don't benefit from burning high octane fuel, and therefore you will pay at least $20 more per tank for no additional performance.
This statement is making no reference to marginal driving conditions, and so is implicitly assuming "normal operating conditions" for the vehicle, and comes to the same conclusion as the other answer: no benefit.
And while we're at it, this:
higher octane fuels actually contain slightly less energy (they just offer a more controlled burn that higher compression engines can take advantage of).
...is also correct, although the energy margin is very small; less than 1%.
While the deep engine theory, and organic chemistry, and physical chemistry, and thermodynamics of it all is a fascinating topic, and I would gladly add to it if there seemed to be a need, in the end our result is the same:
Under the specified conditions, assuming a properly-running, naturally-aspirated engine system, higher-octane gasoline does not improve towing power.
As soon as you add turbocharging, overheating, dirty injectors, fouled plugs, or other conditions adverse to properly controlled ignition, then you've changed the equation, and you might need to step up the octane rating to prevent problems.
Practically speaking, there's a fair chance you'll encounter pinging/knocking conditions during your trip. I recommend using high-octane gas as insurance during the mountain legs. If you really prefer to stick to regular gas, take a bottle of octane booster as a backup option.
My background: FAA certified Airframe and Powerplant mechanic.
Also, I love my turbo-charged Subaru in the mountains.