The problem is that the Fair Labor Standards Act, which defines employees, doesn't follow that old and traditionally known "control test" for determining if someone is an employee.
Instead, they move more in the direction of the "economic realities" test which looks at: (A) the extent to which the work performed is an integral part of the employer’s business; (B) the worker’s opportunity for profit or loss depending on his or her managerial skill; (C) the extent of the relative investments of the employer and the worker; (D) whether the work performed requires special skills and initiative; (E) the permanency of the relationship; and (F) the degree of control exercised or retained by the employer.
Control is considered, but it's not to be given too much weight at the expense of considering the other factors. When courts have looked closely at these factors, the economic reality test really comes down to the question of whether or not the individual worker is dependent on the employer for their livelihood.
On the facts you've outlined, while it is certain that these individuals have some independence, they really entirely on your business for their livelihood. You have a set schedule, you provide their supplies and their income is directly connected to the output of your business.
While I agree that the IC and employee question is full of grey areas, with various entities conducting their own analysis of this question, I would not counsel one of my clients to continue treating these individuals as IC's. The issue of classifications is becoming the main basis for DOL complaints against employers, as of late.
Here is a very comprehensive article from the DOL itself, explaining the economic realities test.
Just to summarize the issues though, I'll walk through the facts you outlined, in light of the factors.
1. Is the work done integral to the employer's business? I think this clearly falls on the side of employee. If you run a barber shop, then the cutting of hair is integral and central to that business.
2. Does the worker's managerial skill effect their possibility of profit or loss? This also falls on the side of employee. Your prices are set. Certainly, the manner that they do their job can effect their tip, which contributes to profit, so this could be seen as slightly in the grey area.
3. How does the worker's investment compare to the employer's investment? Here you may show more investment by the worker, if they pay for all their own equipment; however, that has to be considered compared to your investment. Courts have held that providing one's tools alone is a small relative investment when compared to the total business investment. This could also be in the grey area, but given that you provide the building, billing apparatus, advertising and supplies, this falls more on the side of employee also.
4. Does the work performed require special skill and initiative? This is in your favor as a licensed worker is seen to have special skills. If they also are in charge of getting their own appointments, that can be seen as initiative.
5. Is the relationship permanent or indefinite? You didn't note that these agreements were for a short or set period of time. An open ended agreement leans in favor of it being an employer/employee relationship.
6. What is the degree of control? You set a minimum schedule, control their location of work and their prices. Are they permitted to work at other locations if they wish (for other competitors) when they are not on your schedule? These things lean toward control.