Well, there is data of tests of APCR and APDS.
But I don't know any comparisons of the same penetrator being used in APDS and APCR. Of course you can compare the test results of actually made and used ammo. But this will not give you the answers you are looking for as there are too many variables that differ.

There are also no reports from WW2 that suggest the behaviour you asked about in the amunition types used.

We know the penetration capability of APCR has been superiour to APCBC and APDS has been superiour to APCR. We also know that some early ADPS has had problems with deviation. Which where not severe enough to prevent its use though.
Everything suggests that APCR and APDS worked as intended and did so reliable. So both have been concidered an improvement over APCBC.
APDS was the generally superiour concept and was widely adopted after the war. Mostly replacing APCBC and APCR. The latter only remained for specific uses usually in medium or small caliber weapons.
Given the lack of any evidence or sugestion that you theorie is true there really is no other way than concidering it false. At least until evidence appears.

As a general comment I would add that its of little value to look at isolated statistics or performance data. Even if something like your theorie would be found during testing the question if it matters on a battlefield is an entirely different matter. There are simply to many variable and details different during each incident.

Ok, so in a nutshell the absence of any statements in any known references indicating that APCR was inferior to APDS in dealing with angled armor suggests it was not, or should not be by default considered inferior in that regard, because at it's (Literal) core it was essentially identical to APDS. 

Yes.