This doesn't seem like much of a problem; either leave the extra whitespace out of your source files, or mark the extra lines in some way and remove them before processing.
Version one looks like this:
<TMPL_IF foo><TMPL_INCLUDE foo.txt>
Version two looks like this:
... $in =~ s/\\\n[\t ]*//g; ...
Doesn't this same issue apply to most templating packages, or am I missing something about why this is more of an issue for HTML::Template than the others?