DO NOT .............sell this to a guy who will give you 1/3 of the weight.
Check your local Craigs List (even thought I abhore CL) for services that will PAY YOU for scrap cars. Right now the going rate for a scrap car is around $250 -$300.00 title in hand. (meaning you are the registered owner of the car - no hassles and you sign it over to the guy or give him the title)
Call a few wrecker places and tow yards and ask them what they would give you for it - there are probably SEVERAL of these guys right now in the paper begging for cars to haul for money - and a 1985 LeBaron is not that easy of a car to find for parts (interior) original etc.
Another thing you could do is put it on EBAY - and auction it off AS IS ------whole car, buyer must haul. If you think the buying price s/b $400 for parts - put a reserve on it.
Kidney Foundation, Good Will, American Lung Association, Heart Association - all take cars........and will pick up and give you a tax write off slip - this is great provided you ITEMIZE your taxes. If you don't itemize? Then it's not going to be of any help to you to get an 1800 -2300 lbs deduction.
If it doesn't run? Can't be made to run cheaply? They will scrap the car themselves and keep the money for job services at GW.
You can ALSO call your local HS - auto shop and either ask them if they want a project car or ask a tech school - you can donate it - or see if they will fix it for you cheaply.
Just ideas that roll into my head - I used to have a salvage business years ago - and I made a lot of money doing it -People would call me - say the car has sat for years didn't run------I'd buy it for 50 - $100 bucks, back my tow truck up to it haul it off. Then get back to the shop hit the carbuerator with some engine start, and put jumper cables on it, and fire it right up, Then check it out, do a few minor fixes and sell it to needy families. It was a pretty neat business. Even had a tow truck for repos if they didn't pay. lol.
Best of luck - but 1/3 of the weight? Fooey -------For that? I'd rent a tow dolly from Uhaul, cut the gas tank off myself - and haul it in to the scales & crusher myself. (you have to take the gas tank off) they pretty much do the rest) Unless you can prove it runs - then you don't have to do anything but drive it in.