Not sure whether a whole new piece of software is necessarily needed.
The other big issue is that our process is about setting out two or three things we want to do in a day, and seeing if we can meet our goals.
It would not make sense to click the "start" button on three features/chores/bugs at the beginning of the day, because again it would skew the pivotal data.
I've experimented with both using a separate project for non-engineering (to avoid the skew) but also simply including non-dev work into the velocity with the same rigor that items that offer true value get points and 'cost of doing business' (pay server bill, write documentation) are non-point-accruing chores.
Both work for me.
Our technique is about setting out a good amount of work for the day, and trying to meet those goals. We pull few chores/bugs/features from pivotal and throw them on the board all the time.