I have an epson stylus c82 printer with a continuous flow ink system
(ie ink in bottles outside the printer, from www.inksupply.com, works
great).

The input tray holds about 100 pages of 20# paper. 

I am looking for some kind of modification or accessory to allow me to
run 300-400-500 page long print jobs over night without manually
refilling the input tray.

dear sir...
Here is a nice link to official specs on this device:
http://www.ciao.co.uk/Productinformation/Epson_Stylus_C82__5331876/#Expansion%20/%20Connectivity

The spec says this unit will only hold 150 pages, and it does not
mention there being a large capacity paper tray as an Option. Also,
the spec says the b/w ink cartridge is good for "up to" about 1200
pages, while the color cartridges are good "up to" 420 prints.

So in order to accomodate your request, you are going to have to
"customize" your paper feed tray to hold more paper, but then, you
will run the risk of running out of ink quite frequently, perhaps even
nightly.  If you are printing color, and the ink begins to run out,
the color quality is really going to go down the tubes.

Sounds like your print-production demand is now exceeding your
print-capacity. If you are only printing B/W and not color, then there
are Laser Printers from companies like HP and LEXMARK that print A/B
sz and offer 500-sheet and larger capacities. We have been using
LEXMARK Optra N and LEXMARK W820 network printers with very good
success, and they have stood up to wear/tear very well.

I would suggest 2 ideas.......
1. Research the LEXMARK product line and see if they produce a
mid-volume color printer to replace the one you have.
2. Research the market for a Color Copier that has both copier and
network-printer capability.

If you really intend to use the device with that much volume every
night, you should be able to justify the higher cost of a mid-volume
color printer or copier. Then you would not have to worry about
running out of either paper or ink frequently.

Thank you for your interest.

I basically have an unlimited supply of ink because I have external
ink bottles feeding the cartridges.

I do not see the reference to an optional large capacity paper tray in
the link you provided.

Personally, I would never leave a printer or other machine unattended
for long.  Between potential problems with paper in and out and ink -
despite your external bottles -  I wouldn't trust any printer to
function perfectly for 300 + copies.
And you have to "catch" them too, without their smearing.

This site (German) tells that it is a pretty fast printer  -
22pages/minute mono-chrome -  so I expect that you are wanting to
print in color ("bottles" of ink).

http://www.zdnet.de/enterprise/peripherie/0,39024677,10003112,00.htm

Just another free comment.
Your question as not yet been "answered".
Myoarin