Hi Stu,
>> How can I manually set any of the settings on the "Performance" tab?
It's literally impossible to answer this in a reasonable space Stu. I have no idea what you've done to the server and each feature takes a bunch of code, sometimes quite sophisticated code. And ultimately some of the settings will have no effect on your site anyway - again depending on what you have done.
What I would do is look at the recommendations made by GT Metrix, considering each one in turn and then attacking that.
For example, it seems you are serving large images into a small space in the page - in those cases simple make a new image, the correct size, and serve that instead.
you could also concatenate your css into a single file, load your JavaScript async and so on.
Most of all you could reduce the actual amount of stuff that the front page has to load. It's like 3.7 megabytes, just for the front page. That's a lot!
cheers
Bruce