[stack] Code Transformation Problem (possibly monadic?)

I have the following problem, and I would be most grateful for any help:

Given the following sequence of instruction:

a b m [c m d e] f g

I want an automated transform (no matter how inefficient, it just has
to be algorithmic) to rewrite the code so that each instruction
applies to the stack below the top value, except for "m".

The naive transformation would be:

[a b m [c m d e] f g] dip

However, we have a problem because the "m" instruction can't see the
top of the stack.

The next obvious transformation (which doesn't work) would then be:

[a] dip [b] dip m [[[c] dip m [d] dip [e] dip]] dip [f] dip [g] dip

However, consider if "f" is really "apply".

[a] dip [b] dip m [[[c] dip m [d] dip [e] dip]] dip [apply] dip [g] dip

You can see this won't work for the nested quotation. Informally there
is an undesirable nesting of "dip"s.

There is a very close correspondance between this problem and monads
(http://homepages.inf.ed.ac.uk/wadler/topics/monads.html).
This leads me to suspect that the solution has the form:

[a] unit [b] unit bind [m] bind [[c] unit [m] bind [d] unit bind [e]
unit bind] bind [apply] unit bind [g] unit bind

For some value of unit (a monadic transform), and bind (a monadic
composition operator).

I would be most grateful for a solution.

Thanks in advance,
Christopher