Noob Seeks Help Removing Tree(?) Gunk

Help!

Detailing noob here:

The Mini is up on axle stands getting the brake fluid replaced. I found a weeping connection and had to leave it up on the garage last weekend. As a result, the E46 spent the last week outdoors - near our stand of oak trees.

So, this morning during the washing I noticed a lot of gunk on the horizontal surfaces that looks like - well, it looks like somebody spritzed the car with rust spots. Ugh.

After the wash I tried my Klasse AIO, and, while it removes this stuff eventually, it took me about an hour to get everything off just the back trunk deck, and I'm not really sure I've gotten everything off.

My question is, I know I can get it clean but it will take me probably the best part of today to do it.

Is there anything recommended that's slight more aggressive than the AIO for this?

I used to have a clay bar for the Benz and it worked wonders; I am thinking of going to get another one and have a go using it.

Try the clay bar, it should (under normal circumstances) take care of it.