How do I bind a variable for the minibuffer's use?

[Alan Mackenzie]

Hello, Emacs.

How do I bind a variable for the minibuffer?  In particular, I want to
bind text-property-default-nonsticky to include '(separator . t).

The way it is done at the moment (in query-replace-read-from) is simply
to bind that variable, in the hope that that binding will be the one
seen by the minibuffer.  When the variable has a buffer local binding in
the current buffer, this doesn't work - the minibuffer only sees the
global binding.  This has led to bug #23127

Where is the function `current-minibuffer'?  With it, I could create a
local binding in the minibuffer.  Where is the functionality to bind the
default value of a variable?

Any other ideas?

-- 
Alan Mackenzie (Nuremberg, Germany).