or they're forming a legit adj from the noun ginger. Friend : friendly :: ginger : X, where X = gingerly. With a pretty weird use of "ginger", I grant.

Hm. I would see "gingerlyly" as a dittography (or "dittottography", as some linguists ought not to be able to resist calling it, if they are to be consistent). In any case, it ought to be spelt "gingerlily", on the model of SOED-attested "kindlily". But then, of course, it would be confused with "ginger lily", for which SOED has: "any of various chiefly Indo-Malayan plants of the genus Hedychium, of the ginger family, grown for their spikes of showy fragrant flowers".

There are several English adjectives formed from other adjectives by the addition of "-ly". The following are given as adjectives in SOED:

cleanly (with "cleaniness" as a derivative)
evenly (obs.)
badly
goodly
deadly
easterly (etc.)
elderly
fitly (rare)
googly (!)
lightly
lowly
nicely
poorly
sadly
soothly
sprightly (from adj. "spright"; "spritely" is from the noun "sprite")
tiddly (as one of the three headwords)
towardly
weakly
whitely

That should to be enough.

Oops! I meant "That should be enough".

Geoff Nunberg has a post at Language Log on the word gingerly: a NY Times story on Falluja included the statement "it was a gingerly first step," which provoked his automatic resistance.

Mmm, no, it didn't. You've got Nunberg's argument backward (or I have, but I've been over it several times, because it seems so strange to me). What he says is

The sentence caught my attention merely because it used gingerly in what I always assumed to be the correct way, as an adjective.

He's saying that gingerly is, basically and traditionally, an adjective, and the adverbial use results as a haplology of the derived form gingerlyly.

I read Nunberg's article the same was Tim does. Racking my brain for some way to throw in a pun about "gingerly snaps" or "beer" but nothing seems to be forthcoming. "He gingerly snapped to attention"? Weak, very weak.

Quite right -- I was trying to rewrite quickly, and that rarely goes well. I'll fix it. Thanks!

Another common adjective in -ly is friendly; every few months I find myself stammering through some circumlocution in order to avoid the adverb friendlily. Friendly used to be an adverb, as can be seen from the ME letter of Henry (IV?): Henri ... cyng on Engleneloand ... send igretinge to alle his hold ... on Huntendonscire freondlice. (I quoted that from memory and could easily have blown it, but the point is that friendly is here an adjective modifying send.