[saveMT]

I don't consider Doc Fee over $100 to be legit.
So, I would consider that offer to be $30850 + $364 = $31,214.
That's $1,786 off the MSRP, which is 5.4% off from $33,000.

I'd say that's reasonable, but I can imagine aggressive negotiators pushing it to 7% off.
Me personally, don't want the hassle, so I got my Sport Hatch for 4.3% off MSRP, accounting for the fact that the Doc Fee was $500, but I considered that as $400 less discount. That was in April, and the market conditions have changed since then, so it's not an Apples to Apples comparison.

I was mostly happy to get it without them messing with it (no useless accessories, no garbage tint, etc.).

 

[saveMT]

it's almost certain you'd do thousands of dollars better in a private sale

One thing you want to consider is the sales tax reduction by trade-in value.
In many states, including the one OP resides in, you pay sales tax on the (selling price - trade in allowance).
Looks like the OP saved $623.40 in sales tax, so if OP were to sell the old car in a private sale, OP would have needed to get 11,123.40 just to get the same total deal.

Whether it's worth the effort would depend on many things.