line-spacing in the minibuffer/echo area

[Nick Helm <nick@tenpoint.co.nz>]

How do I change the line-spacing in the minibuffer/echo area? And
then, how do I make that change persistent?

I have this in my init.el

(setq-default line-spacing 2) 

which works well for most windows and buffers, but not the minibuffer or
echo area.

I've tried a few things to change the vertical spacing, such as:

(with-current-buffer (get-buffer " *Minibuf-1*") 
   (setq-local line-spacing 2))

and this

(with-current-buffer (get-buffer " *Minibuf-1*")
   (add-text-properties (point-min) (point-max) '(line-spacing 2)))

but they have no effect that I can see.

It's not that the minibuffer/echo area properties are read-only, because
I can change other properties without a problem. This example for a face
text property is adapted from one in the manual:

(with-current-buffer (get-buffer " *Echo Area 0*") 
   (setq-local face-remapping-alist '((default (:height 2.0)))))

This also works for *Minibuf-1* but, oddly, is not persistent.

Anyway, as far as I know, line-spacing and line-height are not valid frame
parameters, so I can't simply add to minibuffer-frame-alist.

What am I missing here?