Redirect all to https://www.example.com - apache

Question

OK, so I know that nearly every variety of this question has been asked and answered on this forum, and many others, but I just can't seem to get it right. My hope is that if I provide enough specifics, including the process I'm following, that someone will be able to spot my error and correct me. Here goes!
The Specifics
Drupal multi-site
Apache web server
Sites provisioned by Aegir
What I want to accomplish vs what I have accomplished
I want to direct all http and https traffic to https://www.example.com. The following examples marked with a + have been accomplished; the one marked with - eludes me:
+ http://example.com -> https://www.example.com
+ http://www.example.com -> https://www.example.com
+ https://www.example.com -> https://www.example.com #redundant, but at least we know it works
- https://example.com -> https://www.example.com
What I'm doing
Each site has a vhost file generated by Aegir, and each of these vhost files contains two VirtualHost directives:
<VirtualHost 0.0.0.0:443>
<VirtualHost *:80>
I've modified example.com's vhost file to include the following code under the <VirtualHost *:80> directive, which has successfully achieved the three working examples above:
<IfModule mod_rewrite.c>
RewriteEngine on
RewriteCond %{HTTP_HOST} ^example\.com$ [NC]
RewriteRule (.*) https://www.example.com$1 [R=301,L]
RewriteCond %{HTTPS} off
RewriteRule (.*) https://%{HTTP_HOST}%{REQUEST_URI}
</IfModule>
The Problem
What I can't seem to figure out is how to enact the https://example.com -> https://www.example.com rewrite. I've tried many examples found on the Internet under both the <VirtualHost 0.0.0.0:443> and <VirtualHost *:80> directives with no luck.
Also, I'm reloading Apache and clearing my browser's cache after each edit of the vhost file. Any insight, guidance or correction would be much appreciated.
Thanks to all!
Edit:
Below is a redacted version of my vhost file:
<VirtualHost 0.0.0.0:443>
DocumentRoot /var/www/drupal
ServerName example
SetEnv db_type mysql
SetEnv db_name example
SetEnv db_user example
SetEnv db_passwd 1234567
SetEnv db_host somedb
SetEnv db_port 1234
# Enable SSL handling.
SSLEngine on
SSLCertificateFile /ssl.d/example/example.crt
SSLCertificateKeyFile /ssl.d/example/example.key
SSLCertificateChainFile /ssl.d/example/example_chain.crt
ServerAlias example.com
ServerAlias www.example.com
<IfModule mod_rewrite.c>
RewriteEngine on
# this isn't working; neither has anything else that I've tried here.
RewriteCond %{HTTP_HOST} !^www\.
RewriteRule ^(.*)$ https://www.%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
</IfModule>
# Extra configuration from modules:
# Error handler for Drupal > 4.6.7
<Directory "/var/www/drupal/sites/example/files">
<Files *>
SetHandler This_is_a_Drupal_security_line_do_not_remove
</Files>
Options None
Options +FollowSymLinks
# If we know how to do it safely, disable the PHP engine entirely.
<IfModule mod_php5.c>
php_flag engine off
</IfModule>
</Directory>
# Prevent direct reading of files in the private dir.
# This is for Drupal7 compatibility, which would normally drop
# a .htaccess in those directories, but we explicitly ignore those
<Directory "/var/www/drupal/sites/example/private/" >
<Files *>
SetHandler This_is_a_Drupal_security_line_do_not_remove
</Files>
Deny from all
Options None
Options +FollowSymLinks
# If we know how to do it safely, disable the PHP engine entirely.
<IfModule mod_php5.c>
php_flag engine off
</IfModule>
</Directory>
</VirtualHost>
<VirtualHost *:80>
DocumentRoot /var/www/drupal
ServerName example
SetEnv db_type mysql
SetEnv db_name example
SetEnv db_user example
SetEnv db_passwd 1234567
SetEnv db_host somedb
SetEnv db_port 1234
ServerAlias example.com
ServerAlias www.example.com
<IfModule mod_rewrite.c>
# these rules work for everything except:
# https://example.com -> https://www.example.com
RewriteCond %{HTTP_HOST} ^example\.com$ [NC]
RewriteRule (.*) https://www.example.com$1 [R=301,L]
RewriteCond %{HTTPS} off
RewriteRule (.*) https://%{HTTP_HOST}%{REQUEST_URI}
</IfModule>
# Extra configuration from modules:
# Error handler for Drupal > 4.6.7
<Directory "/var/www/drupal/sites/example/files">
<Files *>
SetHandler This_is_a_Drupal_security_line_do_not_remove
</Files>
Options None
Options +FollowSymLinks
# If we know how to do it safely, disable the PHP engine entirely.
<IfModule mod_php5.c>
php_flag engine off
</IfModule>
</Directory>
# Prevent direct reading of files in the private dir.
# This is for Drupal7 compatibility, which would normally drop
# a .htaccess in those directories, but we explicitly ignore those
<Directory "/var/www/drupal/sites/example/private/" >
<Files *>
SetHandler This_is_a_Drupal_security_line_do_not_remove
</Files>
Deny from all
Options None
Options +FollowSymLinks
# If we know how to do it safely, disable the PHP engine entirely.
<IfModule mod_php5.c>
php_flag engine off
</IfModule>
</Directory>
</VirtualHost>

Answer 1

OK now I get it with the content of your virtualhost.
This is not valid:
RewriteCond %{HTTP_HOST} !^www\.
RewriteRule ^(.*)$ https://www.%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
Actually you can't use %{HTTP_HOST} or %{REQUEST_URI} in the RewriteRule part
That's why it's redirecting you to a non-existent host, hence the connection refused error.
You should use this rule in the ssl virtualhost:
RewriteEngine on
RewriteCond %{HTTP_HOST} ^example\.com$ [NC]
RewriteRule (.*) https://www.example.com$1 [R=301,L]
And this one in the non ssl one:
RewriteEngine on
RewriteCond %{HTTPS} off
RewriteRule (.*) https://www.example.com$1 [R=301,L]
HTH