Logging interactive input and output without capturing all typed input and control characters

I am trying to log output from an interactive command-line program; units, specifically.

I have tried using tee like this:

units | tee units.log

or script like this:

script -c units units.log

but they both log all the backspaces and tab completions as special characters like this:

You have: 55 horsepower ^G/^H^[[K^M
You want: wat^Gt ^M
    * 41013.493^M
    / 2.438222e-05^M

The manpage for script mentions this issue.

BUGS
     Script places everything in the log file, including linefeeds and backspaces.  This is not what the naive user expects.

I am aware of the work-around with viewing the file using cat and more or stripping the escape characters with col as mentioned here:

http://stackoverflow.com/questions/7152339/format-output-from-unix-script-command-remove-backspaces-linefeeds-and-delet

As well as the perl script here:

http://log.guidoderosa.net/2009/05/another-old-post-which-may-be-useful.html

But I don't especially want to fix an existing log file: I want to avoid creating new log files garbled with deleted input and control characters.

I thought I had fixed the problem using rlwrap, but it conflicts with the units readline functionality, so that it either fails to capture the output, or with rlwrap -a it captures the output but negates the ability of units to use tab-completion. rlwrap -a -N does not help. This is well-documented in the man page:

BUGS and LIMITATIONS
       Though  it  is  flexible, delivers the goods (readline functionality), and adheres to the Unix "many small tools" paradigm, rlwrap  is a kludge. It
       cannot know anything about command's internal state, which makes context-sensitive completion impossible. Using the readline  library  from  within
   command is still the best option.

Is there any way to cleanly log interactive input and output that doesn't mess with the existing readline functionality?

Update: I would be happy with something like

units | col -b | tee units.log

but that hangs while waiting for interactive input. Can this be fixed?