completion_heads_engraver within a bar

[Jim Tisdall]

Relative newbie alert.

I'd like to have the action of the completion_heads(rests)_engraver
*within* a bar --- so that, for example, rhythms that cross over the
start of the 3rd beat in a measure of 4/4 rewrite as two groups of
two-beat rhythms with a tie between them.  (Also, between bars
as before).

I had the idea of changing the time signature to 2/4 (in that example),
calling the completion_heads_engraver and completion_rests_engraver,
and then wrapping that back into a 4/4 time signature.  But I'm not
sure if that's the happy path to take.

(I'd also, for example, like to handle 3/8 time signatures, by rewriting
as 3 groups of 1/8 beat-long groups, with ties between them as needed.
And etc...)

I'm generating "random" rhythms from user input, so this will be a
help.  I've actually got a perl rewrite program that's mostly working,
but then I found the completion_heads_engraver and realized that my
needs might already be met by the lilypond system.  Any built-in
solution or sage advice would be much appreciated.

Thanks for your help, and
Peace,
Jim