I think white paint started being used around 1961 sometime. It is also not uncommon to find sets from the early 60's with white painted interiors on the toms but a maple interior on the bass drum. I had a 1963 set like this once and have seen others.
As for the psych red set, early 1968 saw a bit of a transistion. Ball bat mufflers went to round knobs and unpainted maple intreriors started to become the norm. I would not be suprised one bit if your set was a match of the two types. I want to say around March-April was when a lot of this started happening. Of coarse there was an overlap all the time as Ludwig always used up whatever they had on hand.
Another thing about psych red(and mod orange for that matter since they both came out around the same time) was that it was introduced around June of 1967 yet Ludwig made no offical ad for it until the spring issue of the Ludwig drummer in 1968. Unless Ludwig shipped either color to a store directly, most people were probably not aware that it was available in 1967. John Densemore made mod orange somewhat popular but he did not get his set until Sep 1967. The two colors also missed making the 1966('67) catalog and the next Ludwig catalog came out in 1970('71) so there was probably not a lot of exposure for it. Since neither color probably sold nearly as much as a color like WMP or OBP, then Ludwig may have mixed and matched drums to get them out the door.
I would not mess with anything you have since any 20,12,14 set in psych red OR mod orange is extremely rare. Refinishing an inside could devalue the drum which would be a shame.