I am interested in learning what non-surgical and non-invasive
treatments exist for achalasia.  Has it been successfully treated
using drugs, vitamins, herbs, acupuncture, hypnosis, chiropractic,
etc.  This project requires a search of both medical and non-medical
sources.  (I am aware of the traditional medical treatments which are:
 internal injections of a botox-like agent, dilation and surgical
repair so these are not to be covered in the answer.)

Hi steveng,

Let me begin by saying that the treatment options you have chosen to
exclude are in fact believed to be the ones most effective for
esophageal achalasia. But there's nothing wrong with wanting to know
all the options, so let's see what else is out there.

First, let me give a quick definition of what achalasia is:
"A disorder of the esophagus in which the lower esophageal sphincter
does not relax. The lower esophageal sphincter (LES) is continuously
contracted resulting in chest pain and symptoms of heartburn. This
causes dilation of the esophagus as well as difficulty passing food
into the stomach."
(http://www.gastromd.com/definitions.html) 
Any therapy would therefore focus on lowering the pressure in the LES.

I went about researching this question by dividing it into two parts:
medical and non-medical sources, as you requested. For medical advice,
I turned to MEDLINE (http://www.nlm.nih.gov), which is the single most
comprehensive collection of articles published in medical journals.
Turns out, there are in fact other options, but most of them have
become outdated with the introduction of more effective treatments:

Drugs, other than botulinum toxin:
- Nitrates, such as isosorbide dinitrate
- calcium channel blockers, such as nifedipine
- antidepressants or benzodiazepines.
(- beta-2-agonists, theophylline, anticholinergic drugs)

The first two choices used to be the preferred treatment options
before the introduction of balloon dilatation and botulinum toxin. The
latter has been discussed more recently. You may wonder why
antidepressants are used. We can clearly see that in achalasia, parts
of the esophagus are not working the way they should. However, why
they do this is not yet fully understood. The enteric nervous system
that surrounds the whole intestinal tract is in fact one of the most
complex structures in the body and has been compared to the spinal
cord. Antidepressants are also discussed as a therapeutic option for
diseases like irritable bowel syndrome. For more background
information on this, see this feature at the WhyFiles:
http://whyfiles.org/026fear/index.html. The most effective treatment
of the three ones given would be nitrates. You may already have heard
of them as an effective treatment of Angina. The three latter options
(beta-2-agonists, theophylline and anticholinergic drugs) are merely
listed for reasons of copleteness. They used to be second line options
when achalasia was only treated using medication.

For more information on this paragraph, you should have a look at the
following articles on MEDLINE:

http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9892793&dopt=Abstract
http://jama.ama-assn.org/issues/v280n7/abs/jrv80010.html
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11319064&dopt=Abstract
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7703511&dopt=Abstract
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9706766&dopt=Abstract
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10571593&dopt=Abstract
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10770358&dopt=Abstract

As you requested, I did perform an extensive search on other treatment
options aside from drugs, surgical and invasive procedures. However,
most of the references that I found were very old and do therefore not
meet the standards for current treatment options. As MEDLINE only
lists abstracts of those articles until about 1985, I had no way of
doing in-depth research on some of those citations, i.e. I could not
estimate their efficacy from the text. If you are interested, however,
you may order full-text copies from your local library or professional
services such as Loansome
(http://www.nlm.nih.gov/loansomedoc/loansome_home.html).

Vitamins:

This article lists vitamins as one supportive treatment among others.

http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=1910911&dopt=Abstract

Psychotherapy/Hypnosis:

The following articles discuss the usage of psychotherapeutical
measures for achalasia.

http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7267424&dopt=Abstract
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=4411960&dopt=Abstract
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=4698113&dopt=Abstract

Acupuncture:

The following citations (some of them from Chinese journals) deal with
the usage of acupuncture as a treatment.

http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11100311&dopt=Abstract
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7799649&dopt=Abstract
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=6567732&dopt=Abstract
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7290444&dopt=Abstract

For the second part, i.e. non-medical sources, I went over to using
Google.

What I found there confirms the medical database in most parts.
Generally, all the treatment options discussed above are listed. Some
examples:

http://www.personalmd.com/news/achalasia_100599.shtml
http://www.nlm.nih.gov/medlineplus/ency/article/000267.htm

A yahoo group on the topic: http://groups.yahoo.com/group/achalasia/

If you do a search on 'intitle:achalasia', these and many other sites
will show up.

Regarding alternative treatment, the following sites seem worth
mentioning:

This location sees a beneficial effect in acupuncture treatment for
achalasia.
http://www.vin.com/VINDBPub/SearchPB/Proceedings/PR05000/PR00003.htm

Acupuncture lowers the LES pressure according to this article:
http://www.rccm.org.uk/ciscacu95-98.htm

This link discusses the possible relation of achalasia to
psychosomatic disorders such as anorexia:
http://www.ltspeed.com/bjblinder/anmeddis.htm

According to this doctor, most cases of achalasia can be traced to a
hernia, i.e. abdominal structures that have been dislocated into the
thorax.
http://donn.lbl.gov/achalasia/views.html

To summarize everything for you: in my view there is not sound enough
evidence to be found on the net to conclude that there are effective
and working alternative (i.e. non-surgical, non-invasive, non-Botox)
treatment principles for achalasia apart from the drugs suggested
above. Acupuncture may well be worth a second look, though.
Psychotherapy may function as a supportive treatment.

I hope this was helpful to you. If you would like me to do further
research on any aspect of this answer, please do not hesitate to ask
for a clarification.

Best regards,
searchbot-ga

A very good job... right on the mark in addressing my inquiry.