Hello Matt,
To answer your first question. Yes I find these plugs regularly in my tanks soon after copulation, either the same evening or the day after, the only difference with this particular time was the size of it, it was exactly the same colour, consistency and dare I say it was odorless ......yes I stuck my nose on it! Stingray sperm has no smell.
In many peoples systems they go with the bare bottom option, because of this any plug( call it what you like, I call it a plug) will quickly be detected and taken in the mouth, much of which will be ingested the rest becoming water born showing as small white pieces/ particles floating in the tank. I use a fairly large gravel albeit smooth which holds it to the bottom for longer plus some quite intricate drift wood pieces that often catch largish pieces up to 1" diameter or more. Given the amount of tanks and rays I keep and breed the chances are far greater for me to come across these things more than anyone with a single large tank, in many cases one with numerous other fish in also, fish love it, they eat like we eat ice cream! hence the reason its not often found in its larger more solid state.
To answer another one of your questions. The term plug is used with both fish and reptiles, certainly by hobbyists . I have kept and bred many reptiles throughout my life also, from relatively common stuff to the more specialist inc Rhino iguanas (Cyclura sp) and many Monitor lizard species (varanus), sadly I never got past the egg stage with these Lizards but I certainly witnessed plenty of sperm plugs along the way. The plug is nothing more than a byproduct, a carrier of the sperm which once it has done its job is simple ejected. Come on how many of you reading this have seen a large white blob hanging from the cloaca (vent) of your females? some have described it as cheese as well as other things, I have seen it hundreds of times on this forum, it usually comes out in 3 or 4 sizable pieces, however when your female is 22" across her disc everything comes out bigger!
The stringy deposits seen floating around the aquarium is something most people see, this is normally coupled with a slight milky appearance of the water, if you do see this then its a pretty good sign the male has very recently done the deed or if not has just missed the spot due to his inexperience with the ladies, normally he will hit the spot within 24 hours or there about's with his second attempt.
Matt your not wrong in your thought of what you "think"you saw from the photo, large masses such as this could easily be mistaken for undeveloped embryo's etc, god I have had a few of those in my hand too over the years, if I there were any doubt in my mind as to what this white creamy substance was I would have asked the guys on this forum if they had seen this before, I've been in the fish game for many many years now but believe you me, I'm not too proud to ask questions, new things keep cropping up to challenge us as aquarists, he or she that thinks they know it all has no place on forums like this one, learning new things makes our hobby beautiful!
I wish you all "very" happy new year.