After putting up with broken search for years, I've finally implemented Google's Programmable Search Engine.
You can customize the look of the search bar & results, remove Google branding (mostly), and pay $5 per 1,000 searches to remove ads. It's super fast and looks pretty good.
Really disappointed that Squarespace let this issue persist for so long. Not to mention their implementation of the 7.1 version (I'd have to rebuild from scratch). I'll be moving to a different service at some point in the future when I can carve out the time.