You have the basics down, and sound like that you can probably sort of everything on your own eventually.
If this is a cost-driven decision, and if you can live within the constraints of your current solution or LogMeInPro, that will be the lowest cost.
If you want someone with the necessary skills to accomplish a custom setup for your practice, you should expect to pay $125-$200 per hour, and that work will probably be between 3-6 hours at a minimum.
There are significant cost pressures in healthcare, and the culture of expecting professional services to be priced as a commodity, be it medical, technical, or business has led to professionals to retire or leave the market in response.
If you are looking for an inexpensive one year solution, stick with one of the existing market solutions.