I've seen various threads on setting up various discounts with newsletter configs but I can't seem to find anything about setting up something that sends a unique discount code for one-time use if people sign up to a Mailchimp newsletter.
Is there anything I can check out that would do this as I don't want a single "static" discount code to send out as they tend to just end up on voucher code sites?
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Personal Discount does exactly what you need. It generates one-time use discount codes for people who sign up for your newsletter. My app integrates with Mailchimp (and many other email marketing providers) enabling you to send the unique discount codes in your welcome email.
I'm happy to help if you need any assistance with setting it up.
Only downside now is that we have other discounts running and offers for half price product upsells etc and Shopify only allows one discount code at checkout which is deeply frustrating.
Totally agree. Unfortunately, it's a limitation of Shopify that customers can't stack discounts. Apps can't change how discounts work (unless an app completely replaces the checkout page, but it's a ton of work - payment processing, PCI compliance, etc).
There is a long thread about it here: https://community.shopify.com/c/Shopify-Discussion/Multiple-discount-at-checkout/td-p/473968