#32 -- I hesitated over the word "oily". High in fat content is what I meant. I've seen "oily" used to describe high-fat fish e.g. bluefish. It doesn't mean that they actually drip with oil.
#31 -- Googled images of elvers and loaches (There are are a surprising number of people named Elver, by the way) and they definitely weren't loaches, which I don't think we have this side the Atlantic anyway. I'm pretty sure they were elvers.

FACTOID: Don't eat too much...Henry I of England died of a surfeit of lampreys.
JOKEOID:
Q What's forty feet long and smells of piss?
A A 'conger' in an old folks home.

Appreciate that recipe, 'turnip, sounds good. Consider it filed under to do.
Vinny #18. Same here. Our elvers are spawned up in the Coral Sea in far North Queensland somewheres and make their way back upstream into rivers and dams.
#33 -- The elvers on Google images all have something grey (a grey back or grey stripes). The ones in Chinatown where completely white, no?

The things in Chinatown were definitely pure white. I'll have to look at Google Images again.
Maybe they were elvers after all. This picture comes from this page, where it is referred to as "glass eel". This page says "Baby eels -- elvers -- start out clear. Bait shops call them “glass eels” around our coastal areas and sell them for bait. Must be great fun putting one of these little greased snakes on a hook." I don't know about that last sentence, but if elvers "start out clear", the things in Chinatown may have been that.
Prepare the eel as above, up to the browning. This time, after the eel has been browned, add to the pan carrots, onions and celery, cut to a medium dice. Cook in the same pan until they just start to soften and the onions begin to get golden. Degalze with a splash of red wine and add a cup or so of fish stock with a bouquet garni. Reduce this liquid by a bit less than half, then put the eel back in the pan and simmer gently until it is cooked through. You can finish it with cream or butter if you like, but I find this unecessary.
Is good with crusty bread or boiled potatoes.