However, 61.113 (b) says a non-CP can fly as PIC "on the clock", so to speak, as long as the flight is "only incidental to that business or employment"... so maybe your friend could hire you to pick up a handful of dirt from Washington for him (or something), and mail it to him from there (remember, you can't carry stuff "for compensation or hire").
Write up a contract where he pays you an amount equivalent for to the flight and return travel expenses.
I'm kidding about that last part, but... technically it would be legal, right?
Sorry, but any attempt to pass off a duck as a pig will ultimately fail if it comes to the attention of the FAA so there's really no point in subterfuge, especially in written form which could be used against you.
Tim's post is exactly correct, the FAA has indicated in the past that they consider "free" flight time as compensation and I'm pretty certain that as long as you can show there was no benefit (besides the experience itself) in the form of financial compensation or loggable hours. There's probably a gray area if you already have enough time to qualify for any rating that the flight time might help with but then you're back to dancing in front of the FAA and NTSB, something I think any sane pilot should avoid whenever possible.
Tom's interpretation is also likely valid. The IRS allows any person to "gift" another person with something like $12000 per year (the amount has varied over time) and technically if you agree to fly the plane on your own dime using your credit card to pay for all direct costs like fuel, oil, tiedowns, etc, the flight would clearly not require a commercial certificate in the eyes of the FAA.
Should the owner later decide to reward you in an amount similar to your total expenses for the trip the FAA will never know and shouldn't really care, just don't put anything in writing that shows a quid pro quo relationship between the flight and the gift.
And finally as others have posted, insurance is a more immediate issue. Your choices are:
1) Go bare (self insured). Probably not a good idea for you unless your friend agrees (in writing) that he will cover any damage or liability arising from the trip out of his own pocket. Even then if his pockets aren't deep enough you will still be on the hook for the rest. And in any case this is a horrible risk for the owner.
2) Have the owner add you as a "named
pilot". This means that he's covered by his insurer (they will pay for repairing/replacing the airplane and for any liability claims). Unfortunately they can still come after you unless you also get a waiver of subrogation
from the insurer (the policy likely limits the owner's ability to grant you that waiver himself). And if you already qualify under the policy's open pilot warranty, being added as a named
pilot does nothing more than providing written evidence that the insurer cannot later claim that you didn't qualify.
3) Have the owner add you as a named "
insured" on his policy. This means you are both covered up to the policy limits, although it also means you share those limits. Alternatively, getting a subrogation waiver from the insurer does the same thing althogh AFaIK that's typically a more temporary arrangement.
4) Obtain your own insurance for "non-owned" aircraft. You might already have this if you currently own and insure an airplane with similar characteristics (same or fewer seats, same category/class, same setup WRT retractable gear, HP engine etc), and if you do have a policy but it doesn't provide this coverage it may be possible to add for little if any money. If you don't have an appropriate policy you can purchase "renter's insurance" in an appropriate amount. Ideally this could be done for just the one flight (assuming you won't be flying this plane again) but that's not likely. You probably could cut the cost by paying for a year's worth and then cancelling for a partial refund (check with the broker on this, it might not be allowed or economical).
Finally, no one seems to have said anything about your own proficiency in this airplane as well as flight across the mountains in the winter. I believe that you are familiar with some RV models, but I'd give careful consideration to what kind of checkout you should receive before launching on a trip across the country in an unfamiliar airplane. Even if you have adequate experience with a RV-9A, it's likely that there are unique issues with this particular example including but not limited to the avionics, engine, and fuel systems.
Thanks guys. 
I think they are jealous.
