What are the most effective ways to reach a dentist, counselor, chiropractor, massage therapist for marketing?

Honestly is not as hard as it might appear to you right now. I have a few Chiro friends and first met one while visiting then through one met a few more... What I've learned is that most practices are small and thus operate very quickly.. They can make decisions on the spot if they like something or remove a system of they don't... Same as hiring their staff...
Call for an appointment and simply let the receptionist know you're bringing in a product to help their office... All doctor visits have a first time meeting anyway.. So getting to chat with you about a product (specially if is actually helpful) might give them a joyful break in their day... Go with a solution and maybe some sort of trial for them to experience it then is just a matter of not necessarily closing them but retaining them through that much smoother "close" via trial...
There's nothing better in a pitch than a free goodie... Also, try having your pitch incorporate an existing user that might be a competitor.. No one wants to be the first but no one wants to be last either so play that in your favor...

First, IMO, each firm has a niche and a ideal client. I'd figure out both those things and they're bound to tell you how to best market to them.

It's way to difficult to try to market to 4 different niches.

Everyone you mentioned is in the medical or personal healthcare profession. The first step is to try and setup a meeting with each type of client you would like. In this case that would mean meeting with a dentist, counselor, chiropractor, massage therapist. See if you can meet with them for at least 20 minutes or so. Ask them their onboarding process for new patients, difficulties in their business, how they market to get customers and anything you can think of study them. You mentioned you have existing client, interview them and get testimonials on how you solved their business problem. Once you fully understand the needs to each business market your service as a solution to those specific needs and use the wording you learned from your interviews.

Think about it, your client is really your client’s client even speaking with potential patients and asking them what their likes and dislikes are about going to a dentist, counselor, chiropractor, or massage therapist can help in marketing to healthcare professionals. Personal contact definitely works when it comes to marketing, send a personal letter to the healthcare professional introduce yourself, follow up with a phone call and point them to your website. If you performed your interviews well and tailored a landing page to that market.