RE: Question on remapping keys

["Drew Adams" <drew.adams@oracle.com>]

    >      (define-key map [remap `,from] to)
                           `[remap ,from]

Right. Thanks, Johan, but that doesn't completely solve the problem. The
result of remapping is this for minibuffer-local-completion-map:

(keymap
 ...
 (remap keymap
        (scroll-left . my-scroll-left)
        (scroll-right . my-scroll-right)
        (scroll-down . my-scroll-down)
        (scroll-up . my-scroll-up)
        (next-line . my-next-line)
        (previous-line . my-previous-line)
        (help-command . my-help)
        (self-insert-command . my-self-insert))
 ...)

This looks promising, but it seems to work only partially. For instance,

(where-is-internal 'my-scroll-up
                   (list minibuffer-local-completion-map))

returns ([remap scroll-up]), which looks good. `M-x' followed by `C-v' does
invoke `my-scroll-up', but `M-x' followed by [next] (also bound to
`scroll-up' in `global-map') does not invoke `my-scroll-up' - it invokes
`next-history-element', just as in vanilla Emacs.

IOW, apparently not all bindings of `scroll-up' got remapped. I'm looking
for behavior similar to that of `substitute-key-definition':
remap/substitute _all_ bindings. This is especially important since I
apparently have no control over which single binding gets remapped - that
is, only one binding of the command seems to be remapped, and I don't know
how to pick which one.

Similarly,

(where-is-internal 'my-help
                   (list minibuffer-local-completion-map))

returns ([remap help-command]). That suggests that `help-command' was
remapped, but using `C-h' in the minibuffer does not invoke `my-help'.
(Why?)

If I use `substitute-key-definition', providing `global-map' as the OLDMAP
arg, it works perfectly, but the performance is unacceptable. There must be
some way to do something equivalent using command remapping (?).