I'm pretty sure (although I was there, I didn't notice it at the time) that the F-4K first-flight markings were not the same on the left and right sides.
The right side of XT-595 was marked "McDonnell" in red outlined with white and a big " NO. 1 F-4K" underneath that.
This was subsequently painted over.
I'm pretty sure that the left side did not have the markings on the mid fuselage. Instead, a small "McDonnell" and "No.1 F-4K" were marked on the nose, I believe using temporary paint that was subsequently washed off.
RAM Decals 72-001 includes the markings for XT-595 (http://www.rammodels.co.uk/product_info.php/products_id/358/osCsid/a7a1df94887553fc4e1decf0e9b5011f); note that they have assumed that the markings were symmetric and therefore present during two different time periods, which I think is incorrect.
There were at least two small difference between XT-595 and production F-4Ks: the rear cockpit had throttles (but not stick or rudder pedals) and the fuel vent aft of the rudder was 'flat" rather than the V configuration (see http://tailhooktopics.blogspot.com/2012/05/spey-powered-phantom-changes.html and scroll way down). It also had the Mk 5 M-B ejection seats with the metal sugar-scoop parachute containers; I'm not sure when the Mk 7 was introduced.
The flight test team included me, easily identifiable as the youngest member, only a month or so out of college.
Joe's book, A Sky Full of Challenges, is only available from Amazon as an expensive used book.
It used to be available directly from him (see http://www.omnishops.com/TestPilot/) but Joe died last year and the link to order doesn't work. However, it appears to be available as an ebook: see https://www.smashwords.com/extreader/read/142339/1/a-sky-full-of-challenges