I'm not sure the extent to which people have looked into James Alefantis's past/family, but I thought I might as well share the little bit I've found in case it's of any use. It's all pretty insignificant in itself, but perhaps it'll fit in somewhere and/or lead to further areas of investigation.

Here's James A. Alefantis on intelius: https://www.intelius.com/people/James-Alefantis/Mc%20Lean-VA/0CT822NHKG0

Additional search results for the name Alefantis:

https://www.intelius.com/people-search/Alefantis

https://www.peoplesmart.com/default-name-results?Find=alefantis&LastName=alefantis&State=VA

https://www.ussearch.com/search/people/~/~/alefantis

(Note that in the ussearch results it lists Ping Pong Productions and Transformer Gallery as places at which James Alefantis has worked. I know Transformer Gallery has already been talked about to some degree, but I'm not sure what the status is on Ping Pong Productions.)

Achilles Alefantis, Helen Alefantis, and Louis Alefantis are among the names that come up listed as relatives of James Alefantis. There seem to be at least two Louis Alefantis; both Louis G. and Louis J. Alefantis come up.

Here's Louis G. Alefantis's obituary: http://www.legacy.com/obituaries/buffalonews/obituary.aspx?n=louis-g-alefantis&pid=1292379

Here's Helen Alefantis's obituary: http://www.legacy.com/obituaries/buffalonews/obituary.aspx?n=helen-alefantis-rappas&pid=87763024

Helen Alefantis on nyabandonedaccounts: http://nyabandonedaccounts.com/r/EPBxA/HELEN+++ALEFANTIS/3735+DELAWARE+AVE+APT+208++KENMORE+NY+14217

Achilles Alefantis on nyabandonedaccounts: http://nyabandonedaccounts.com/r/4Gvx1/ACHILLES+++ALEFANTIS/145+EAST+48TH+STREET+APT+21-D++MANHATTAN+NY+10017

A search for the name Alefantis on missingmoney.com brings up several Alefantises, including Achilles, Helen, James, and Louis J. http://imgur.com/a/UFqRq

Random thoughts:

I was surprised to find other Alefantises. I'd gotten so used to seeing posts about how the name James Alefantis is suspiciously close to J'aime les enfants that I was assuming it wasn't his real name. This still doesn't totally make sense to me.

There are addresses in NY associated with Achilles and James Alefantis. Maybe this is already being looked into, maybe it's irrelevant, but it's the first I've seen of it, and it got me wondering about possible NY connections.

I saw it alluded to in another post earlier today, but the scarcity of search results for James Alefantis pre-2016, the fact that this is all I can come up with, even after an admittedly cursory search, seems, at least to me, truly strange.

At any rate, hopefully something here will be of some use.