Having done several hundred cases with Acceledent®, I can attest to it's safety and effectiveness. Unlike other appliances out there with claims of faster treatment as a benefit, safe acceleration of tooth movement is the entire basis for FDA approval. Quite simply, if the claims weren't proven, the product wouldn't exist as an FDA approved device in the market. I don't get why the orthodontists you mentioned won't recommend it or say it is not proven, other than not wanting to purchase and stock an expensive product (it retails at ~$1000 USD). It certainly doesn't make teeth fall out faster. We are very clear on the biologic effect of Acceledent and it actually would make teeth less likely to fall out (the same technology has been in existence as an osteoporosis treatment for decades). I have actually used it on quite a number of patients with severe bone loss specifically to make tooth movement healthier for them. There are numerous studies coming out now that are more clearly elucidating how this and similar appliances actually make tooth movement healthier in general.
Invisalign is a tool for developing a beautiful smile like any other. It is good for certain tooth movements, but is less efficient for other movements. Every patient's treatment needs to be individualized to their goals and their face. Sometimes Invisalign is a good idea and sometimes it is not, but I wouldn't use the word "can't" for tooth movements than can be achieved. Through time consuming review of your ClnCheck by your orthodontist, proper staging and force application can be prescribed into your computerized tooth movements to move teeth vertically within reason. Additionally, with the use of TADs significant intrusion (another type of vertical movement) can be achieved with Invisalign. That said some types of vertical movements (and horizontal ones too) can be difficult with Invisalign. I wouldn't let New Beauty decide what type of treatment I need. See an orthodontist experienced with Invisalign and let them help you reach your goals for a great smile.
Without radiographs and photos showing me how the position of your teeth factor in to your facial appearance, I am afraid it is hard for me to tell you what treatment would be best. The impact of the positions of your teeth on your smile and on your facial appearance can be dramatic, and there has been a greater shift towards facially focused orthodontic treatment in recent recent years instead of simply lining teeth up. If you are simply wanting to get your teeth straight, both treatment plans will likely accomplish that, but there are many more factors to a gorgeous smile than just straight teeth, and although both plans contain some compromises (with good reasons that your orthodontist can discuss with you) the Invisalign treatment is probably not a good idea for the following reasons:
Moving your teeth and the changes (hopefully good) to your smile are a big deal and it is perfectly normal that you might be feeling nervous about the process. People change their mind all the time, so I am sure your dentist will understand. You can stop treatment at any time, but before deciding whether or not to continue I'd speak with your dentist about your concerns and maybe they can put you more at ease. Keep in mind that your dentist has already paid significant lab fees to Invisalign to have your aligners made, so it is unlikely you'll get a full refund.
I'd call your orthodontist about your broken bracket so they can get you in to bond a new one. They'll be able to tell you if you can continue to wear your rubber bands without the bracket on. They should be able to squeeze you into the schedule fairly quickly for a broken bracket so your be good as new in no time.