Hi, Fredrik. I am happy you asked this question, the short answer is, go for it, it won't take you too long to launch, and you can get very great metrics out of that, like conversion rate, SUS, etc.

You can use Google analytics to compare the before and after, because you probably already have numbers, like how the product is performing now, how many members sing-up per month by using the website etc. So you can compare what you have to after your improvements. And don't forget, you don't have to apply UX tools that aren't necessary. When a recruiter look at your portfolio project they wanna to know that you are capable of improving a product, and that you can apply the right tools. that's all. You don't need to start a product from zero, like a huge App (I did it and I don't recommend), because most of the companies will hire you to work on already existing products, and only on small pieces of it.

I have seen many UX portfolios that has website projects and that's fine, as long as it has improvements.

I will have an article coming soon about this subject as well.

I Hope that could help a bit.

Cheers!