No such thing as a "dedicated master" - a master tape is a master tape. There is only one. There is no 'special sauce' master tape redone from the multitracks for AP or any audiophile label - that would be a remix anyways.
It is absolute rubbish that anyone would hand check 1500 or even 500 pressings! No one does that. They come from the pressing plant in sleeves and sealed. No one reopens them, pulls each one out of the sleeve, and reseals them. No one.
Rhino gets test pressings. Everybody does. How many is a matter of how many the label pays for. Take a look at Discogs to see how many TP's are for sale. Tons. They get distributed fairly heavily, internally and externally. People don't listen to TP's for the sound. They listen for pressing defects that generally come either from plating or another physical flaw. A test pressing has nothing to do with the potential for, or presence of pressing defects in the production run. That is completely separate from producing the TP's.
Artists and producers may listen to the TP for sonics. But if they don't accept it, it goes back to the masterting studio - not the pressing plant, who cannot alter the sonics - after all, that is in the lacquer or digital file they were sent.
There are no higher levels of QC at RTI or any other plants. They don't stop the press every few copies to check visually. They do inspect every pressing run by taking out a few random samples and checking them for obvious visual flaws. It's a factory - their QC is standard, as are their prices.
Rhino have done a ton of fabulous all-analog reissues, in fact, more are AAA these days than in the earlier days. And, for a long time Rhino used the disatrous Rainbo - for most of the past decade, they have primarily used RTI. Rhino vinyl has actually increased in quality, and value for money.