Could you remain in a consultant role with your current employer while you work another job?

Personally, I'd move on. Life is waaay too short to limit yourself out of a sense of obligation to an employer who isn't using you to your full abilities and has no growth potential. Find you a new career opportunity, and let someone else move into your starter position! If you hate the new job, then you look again and try a different one.

Loyalty from an employer can only be from the perspective of what is in the best interests of the company. Therefor loyalty from an employee must be from the opposite perspective. Employee loyalty can only be from the perspective of what is in the best interest of the employee.

Companies preach the mantra of loyalty up until a down turn then all bets are off. I learned this lesson rather painfully 8 years into my post college career not long after I received my second in a row performance review appraisal rating of 1. 4 of the previous 6 performance reviews were 2. The first one I got a few months after I started with the company was a 3-New to Job, and I got a 3 in year 4 during a major disconnect period with my then boss.

I am still a loyal employee because I do not go to work for employers I do not seek the opportunity to work for. However, I am only as loyal as my financial and advancement opportunities allow within the context of what is best for my family.

In my career I have worked for 7 employers. The first was my own company that I started with several investors (5 years), the second was a college associate engineering job I did while finishing my engineering degree after selling my business (2 years), the third is the company I mentioned above (8yrs), I then did some consulting (less than a year), the fifth company I was with as a get in out of the cold job after the RIF while my bride finished grad school (2yrs). I left for a major advancement opportunity, and the 6th company I just resigned from last June after 10.5 years when they exited the JV company they had sent me overseas to start with a partner company. Since they did not have a key role for me and offered to put me on unpaid LOA for several months before a role was expected to open up I went to work for a competitor who had been courting me for about 3 years.

I never have a stale resume. I keep mine updated and test the opportunities available in the job market periodically to see how I am received. I use personal networking as my primary method for testing the market and I also use LinkedIn which is a good tool to keep your networking active and your network serviced and to get in front of interested employers and recruiters.
Accounting is a hot field. I suggest that you keep a fresh resume at all times and test the market. You may find that you can make a notable move that offers similar job flexibility and gives you advancement and financial opportunity. Have you taken the CPA exam yet? If not, that is a good move. Or the CMA, CFE, or CIA certs.

Good luck.

I have worked for small and large companies. The only time I quit a job was when I saw I was going nowhere at a small company. Two people retired and they hired a family friend from outside the company and a man that had been there 5 years longer than me and I worked circles around him.
Small companies play by their own rules. That's the freedom you feel. Just because you feel loyal to them doesn't mean they feel any feeling of "they owe you for your loyalty and hard work".
Larger companies have their flaws too, but in my experience they are more likely to move you up and pay you more because their is room for growth and places to go.
Indeed.com is a great site.
I also like moster.com, careerbuilder.com, simplyhired.com, and glassdoor.com. Glassdoor has sample salaries from past employees and reviews of what they thought about working there (I have used glassdoor even when I was just thinking about another job, or offered a job at a competitor's before I committed to an interview).