There is no way to change the graphics chip, so we can discard that as a possible idea.
I was going to take a couple of snips of the inside of the laptop, but I found this page, which covers about everything we have discussed in this thread.
Y560 overheating and shutting down - Lenovo Community
Frankly, sorry pour cold water on the subject, but I am thinking that your only alternative is, as in my first post, use it as a typewriter and buy a better laptop.
One thing I don't understand, however, is why you should get a temporary improvement and it then deteriorates again. The thermal paste would have been just a thin smear. Sorry if I talk down to you, but you did, of course, apply it between the CPU and its mounting base? My suspicions were aroused by your wording: " applied it
to the gpu and processor "
Other than these ideas, I have run out of any further suggestions - sorry.