Hi there, 

A few quick notes on your page: 

1. Copywriting - I admit, I’m not your target market but the copywriting on the page is really missing the point. I re-read your post here 3 times and looked over the page 4 or 5 times to even begin to understand what you are trying to offer. 
   
   “Less chair-time for your patients means more profit for your practice”  - Your headline is the only piece of copywriting for the first 2/3 of the page. It also has the added benefit of being vague. You have to keep in mind dentists are busy. They have practices to run. Employees, vendors, insurance to deal with. Unless you really capture their attention in the first 2-5sec...they are gone.  
   
   There are probably 10-12 other elements on the page that fail in their role at convincing me YOUR product is the best for my practice. OR it can save/make me money. OR it can save me time. 
    
2. Design - Again… missing the mark here big time. Even a template would be better. Contrast and colors are off. Fonts. Sizing. It looks like something that was put together in about 3min without much thought for conversion design. 
    
3. CTAs - This might just be because you copy over the page to show it here without affecting your traffic/conversion stats. All of the CTAs below the fold do nothing when you click them. 
    
4. Data - It seems like you don’t have any data/analytics on the page. It means you are working in the dark. Trowing a few things at the wall and “guessing” what sticks. Get some GA on there and some heatmaps/screen recordings. My gut felling is you lose 50% of your traffic right away due to design. The other 25% drop off in the first 10sec. Most probably don’t scroll more than the 2nd or 3rd section down. BUT that’s just a guess. You don’t know either because you are not tracking anything. 
    
5. Demo/Form - This ties back to the copywriting/design but it’s important to highlight it as well. Do you want to take a guess how many people/agencies/sales reps/etc. are trying to get on a dentist calendar… 10s and in some cases 100s… per day! There are plenty of blog posts and youtube videos how to make a great signup box so I won’t rewrite it again here. But do some research. Find more interesting/engaging angles that you can try out. 
    
6. Message Match - Last on the list… you’ve mentioned cold email traffic and social ads. I don’t think you should be running social ads to this page until you figure out 1-5 above. I haven’t seen the actual emails you sent out but I have a feeling there is a message mismatch between the copy in those emails and what’s on the page. Might be wrong. In any case, make sure the copy in the cold emails resonate on the LPs as well. 
   
   Also… you’ll need different LPs for your cold email traffic and for your social ads. It won’t work well with one page for all different types of traffic. 

However, you hit on something in your original post that would help you make this 1000x times better: 

“Clear Aligners are a complex product, and we find that most doctors are very happy to be able to talk to one of our Orthodontists once they take the time to book a demo with us.” 

and once again on the LP: 

“that can discuss your pain points, and how Clearly can help improve your experience working with Clear Aligners.”

Get on those calls and listen. Take notes. - Your ideal customers are telling you exactly what they want, what their pain points are and why you might be able to help.
 

Where are the pain points on your page?

Record them if they give you permission. Re-listen again and write your landing page copy based off of what they tell you. 

Here are some thoughts on your page:

First, I second what @Hristian  noted already. Rather than repeat that advice, I’ll try to build onto that advice.

I think the biggest impact will be clarifying the offer. Look at the hero section. The button is the only thing that says demo, and it’s not clear what it is a demo of. Even the heading of the form doesn’t have it. It’s just a generic “contact us” section. Why should the user contact you? Make use of the form heading and lead in to clarify the offer a bit. What is the benefit of the demo for them? What are they going to learn/see?

Use the headline to tie carry over the messaging from the email bringing the user to the page and tie it into the offer.

Also, don’t try to sell the product in a generic way. Don’t try to sell it at all here. Instead, sell the offer. Make people want to learn more, and anticipate the demo.

Try to make your CTAs more consistent throughout. You have “Book a Demo”, “Get Info”, Book a Call” and “Talk to One of Our Orthodontists”. That’s confusing for users and weakens to offer.

There is too much “we” copy, i.e. “We work with,” “Our aligner system is very simple…,” etc. Make it more about the user and less about yourself. 

I think the information should be reordered. The social proof is good, but it doesn’t have the same impact if people don’t even know what the product or offer are. Touch on the benefits and features first, then use the testimonials to add credibility to that. And I would remove the “So, what are you waiting for?” section all together. It’s too easy for the user to provide a valid answer in his head and stop right there. You’re validating inaction.

Hope that helps. Best of luck!