So essentially, I'd need to get the email address of whoever is actually making the offer and send him/her pictures of my car and scans/copies of the receipts for the tint and the speakers?
What should I actually say? "I was thinking somewhere closer to $x; I can send you pictures of the condition the car was in and copies of receipts for the modifications I had done if you'll give me your email address."
Exactly. Let them make the offer and then you counteroffer. But remember you have to give them something to work with, but don't overestimate yourself. You need to know how much the modifications add to the value and you can research the value of the 'condition' of the car. Mileage is something you can't change but you may be able to sway them that your car was in better than average condition for the mileage it did have, and more importantly in better condition than the baseline comparison.
If they do negotiate it will be somewhere between their initial offer and your counteroffer. The best way is to be firm while being fair. It's tit for tat. You have to be willing to negotiate yourself. You can't just ball up and expect them to yield. If you do reach an impasse, ask to speak with their manager as a last resort.