I blame textbook authors and publishers for part of the problem.
The usual practice is to use "conversion factors" so as to be able
to write a conversion on a single line and eliminate the writing of
the individual equivalences that are used.
For example, the conversion of 1 m to inches might appear as
1 m ( 100 cm/ m)( 1 in/ 2.54 cm) = 39.37 in
[ the fractions would appear with horizontal fraction lines,
and the cancelled units with slashes. ]
This practice also presents what is essentially a multi-step problem
( a notorious challenge to weak students) as a single step.
I fully endorse Robert Cohen's approach of "unit replacements"
To amplify on that approach, the basic idea is to
"treat the units abbreviations as algebraic symbols",
and to do one conversion at a time.
The above conversion might then look like:
1 m = 1 (100 cm) = 100 cm
1 in = 2.54 cm
so cm = in / 2.54
100 cm = 100 (in /2.54) = (100/2.54) in = 39.37 in
In this format it is easy to scan up and down to check the steps.