There are always problems trying to balance two jobs. Unless you work some kind of shift that gives you some leewya in work hours at your current job, you will only have your "free" time(lunches, nights, weekends, vacations) to pursue consulting.
It sounds like you want to keep your full-time job until you essentially become self-sufficient as a consultant.
Your problem is that your are not going to be able to build any type of steady customer base if you are only available to work at night or on weekends (when most small- to medium-sized businesses outside of retailing or manufacturing AREN'T working).
You will also have NO chance of becoming self-sufficient (nor will you be considered a serious consultant) if you gain a reputation of only being available at night or on weekends.
And don't forget that initial impressions (on which most reputations are initially based) are very hard (and sometimes impossible) to overcome.
Regardless of what shift you work on your current job, when consulting, if you aren't available when your (potential) customer needs you, they will hire someone else.
Your best bet, given your current financial status, would be to find a small company to work for, that provides consulting services, but will still pay a salary (vs. pay you only for hours worked). Then quit your current job. This will give you the security of a full-time job while still getting your name known in the commercial sector.
Hope this helps.