For future self, and anyone else that needs to go down this path, it's actually not as much work as I expected to create a custom Order Editor.

As the docs say you can override the entire order editor by addding a view key to storeAlias.order.editor.config.

{
    view: "/my/custom/view.html"
}

So I simply copied the default order editor that ships with Vendr and bastardized it to my own ends. I ended up moving some of the panels around too which was a nice bonus.

One thing that tripped me up is that you'll need to include all the keys from the default config. Seems obvious in hindsight but knowing this may save you a time. For example:

{
    orderLine: { ... },
    customer: { ... },
    billing: { ... },
    shipping: { ... },
    notes: { ... }    
    additionalInfo: [{ ... }],
    view: "/my/custom/view.html"
}

I'm quite pleased with the outcome, it's great that Vendr allow you to do stuff like this. I'll have to make sure that future changed to the Vendr framework get ported across to the custom template though so something to beware of.