This required some search and replace in strings, which oddly enough isn't implemented in Applescript. But since Applescript can run any shell command, this is easily circumvented. I use the "sed" command, as follows:
set escapedPath to do shell script "echo " & quoted form of MacPathString & " | sed 's/ /\\\\ /g'"
The syntax is "sed s/find/replacement/g source", where g is the regexp global flag. The "|" is the unix "pipe" operator which forwards previous output to the following command, i.e. the "echo" command results are piped into "sed".