After getting word from a member that operating HID lamps in paper lined and plastic sockets is a bad idea, I wonder if these sockets are safe when a HID lamp is operated base down in plastic and paper lined sockets as I have some DIY HID fixtures that use such sockets.

I would never do it myself, but as you said, some members have had success with it. Always be careful, the most preventative you are, the better.

I would avoid the paper lined sockets. The thing is, it degrades due to humidity. It may be just good enough for 120V, but anything above that is too much for me. And HID use either 220+V OCV or even high voltage pulses, so to me off limits for paper insulation.

Plastic is OK as long as you keep its temperature low (below 100degC, to maintain some margin), therefore the base down only position recommendation.

The best from this perspective is of course the porcelain, but there I faced issues with riveted contacts: Because porcelain is not flexible even any bit and has different thermal expansion than the metals, rivets feed through the porcelain tend to loose pressure so contact over time. It is even hard to spot, because when the lamp is out, the contact springs put the rivets under tension so mask out the fact the rivets are getting loose. So be careful with the construction and manufacturer, use only the proven ones.

  There are some single standard sockets most you could put on there is 60 watts. 

 Because of switching points on standard lamp sockets is not made for Hid use and these are not pulse rated.  It  ill eventually screw up switching part of sockets.  Heck I killed a mogul 3 way socket by putting a 1500 watt Incandescent in one 
It would make a loud pop sound when you switch them on.

 It would work but u dealing with heat degrade on plastic parts on the sockets.   Porcelin socket is the best as they can take the heat load. 

   GE did use Bakelite sockets on there mercury nema head

     

Always try and use pulse rated sockets when they're needed.   

Gaash got away with Poybutylene sockets in some early 90s lanterns running 70W SON/I. (Gaash GEC Z8691 with approximately horizontal lamp position, and some posttops with base down lamp). I have a few Z8691's that were removed from service after 20+ years full night operation, and there are no signs of degradation whatsoever on the socket

I've had no problems with plastic sockets. with BU HID up to 175W. Afterall, 660W/250V is a common socket UL-rating even in plastic form. Ceramic is clearly better, but plastic is fine.

There are plastics able to withstand quite some heat, but these materials are used only when really necessary (obviously - due to cost).
So if a socket is explicitely rated for the HID, it is very unlikely it will not work, in any position the lamp is rated for (one of the parameters dictating lamp compatibility with burning position is the base/socket temperature staying within limits, the same limits are then used for the socket design).

The "base down only" and "no paper" here was meant when you (for some experiment purpose) have nothing else than sockets which are not explicitely rated for the given use, so when e.g. using standard incandescent sockets for e.g. pulse MH.
Of course, it is not advisable to use them anywhere out of the experiment setup (you should be ready to respond in a safe manner to situations when the socket starts to fail).

 

   GE did use Bakelite sockets on there mercury nema head

   

GE also used them in the GE M-250R2 and the M-250A2 for a short while as well.