If you can identify and want to keep some of the perennials, then you can dig them up and put into cheap plastic pots for the moment. You can then spray the area with Roundup or generic equivalent, follow the directions. It will take a couple weeks to kill, I beleive.

You said you wanted to do it quickly but I just think about all those precious perennials, which can also have a cost value attached to them if you end up having to redo. For example, since you don't have a specific list of perennials, it could be something as common as canna lily or something a little more precious like a long-lived peony.

Since you still want a garden there, just smaller, I think you can take this season to identify the plants and weeds coming up. For the weeds, take them out when you can.

For the small trees, take them out also if you don't want them to be bigger.

For the perennials, when you identify one you don't want, take it out. If it is something someone else might want, feel free to ask people if they do.

For the remaining perennials in the section that you don't want, see if other people want them.

For the perennials that you do end up wanting, but just need them relocated, then determine how you might arrange them in your smaller plot.

Another reason to wait is that as the plant comes up, you can actually pull it out, now that you know where it is.

If you still want to take them out without waiting this season, but still want to grow this season, then I think you can start digging and anything that is not dirt, put in a pile. You may have to dig as deep as 6-8" depending on the type of perennials you have.

Find your local garden club or cooperative extension. They will come and dig up your plants and put them to good use, saving some former gardener's precious plants. Then you can kill the rest and plant grass.