There are a lot of what are known as "short-belly" spey lines available on the market and they are very easy to find. Short-belly spey lines have a belly (from tip to end of rear taper-i.e. ahead of the running line) of 50'-56'. The exception to this is the Nexcast (Winter Authority) WA 45, which is a head with no rear tape of 45' and is still a short-belly spey line. RIO, Airflow, Cortland, Scientific Angler, Gaelforce, Ballistic all make short-belly spey lines that are easy to find.
You're 13' 7wt rod would be balanced correctly with any of these short-belly lines in a 7/8 line weight.
I use mid-belly lines on my 13' rods. These have a belly of 60'-67' (or in the case of the Nextcast Winter Authority (WA) 55, a head with no rear taper of 55' or a little shorter.
As has been mentioned, casting a short-belly line takes more skill than casting a short, heavy Skagit line or a Scandi line. Anchor placement is critical with the traditional short-mid-long belly lines, as is good "D" Loop formation. But it is well worth the effort (and practice) the learn how to cast the longer, more traditional belly length lines.