I have told people to part out their projects and buy a completed bike as it will save them money in the long run 
But most have some sentimental (real or imaginary)reason to want to proceed 
John
I agree with everything you said except for the quote above, Progress payments are standard in the vintage bike repair and resto trade. Have everything in writing! It may seem over the top to do that, but believe me, down the road you will be glad you did if things go bad. MAKE the owner sign the repair order, estimates and or billings. This clears you if a dispute arises later.
A reasonable explanation about WHY should be acceptable and if not run, dont walk away as you just dodged a bullet.
If the person is fair they actually SHOULD appreciate your diligence and professionalism and I am famous for having "Good Buddy" deals go south so I speak from experience.
Now,,, the above statement about parting out a classic,
NO , NO NO Nein, Nyet, Yok!, NEVER, NO NO NO NO! There are literally TONS and TONS of orphan parts out there, DO NOT PART OUT a Classic under any circumstances! Numbers matching or factory matched bikes are fewer and fewer, and It drives me literally mad to have collected parts for 10-15 and 20 years to restore or rebuild a basket case only to see some F**King Idiot parting out a better example on ebay. Way too many idiots doing that. I have bought up barns full of old bikes to save them from scrappers and fly by night ebay flippers who just want to part them out in the misguided notion they make more than selling it as a whole project or basket case.
Unless its a late model Ducati,,, those bring serious coin even down to the screws and hardware. Some morons rationalize they are doing the community a favor by providing parts. BULL PUCKEY! I can point you right now to warehouses FULL of parts,, I have 3 40 foot shipping containers packed full right here. (I did NOT part out those bikes and been BUILDING those parts INTO bikes.
If you cant manage the project then sell it on to another true enthusiast who will, But dont part out classics.
and if someone needs to see a spread sheet on why parting out a classic does not add up, let me know.
Math,, its Brutal.