That certainly makes it a little more difficult, but I'd still look at a similar setup. Are you opposed to buying used?
It's not worth putting any money into your current platform. While there's definitely gains to be had, the price is staggering. A used i7 can fetch near 300usd. See if you can find a combination of parts similar to the list on the used market, and buy a new ssd. You should be able to come in under budget that way.
What speed and capacity is your current ram? Being a 7th gen intel, I'm assuming its ddr4. If its a good kit of 3000mhz or better, you could save money by reusing. But if it's any slower than that, I'd sell your current setup complete with ram and buy new. Ryzen likes fast ram. Should help offset a large portion of the cost.