Connection Timeout on order submission

-- url of the page with the problem -- : applevalleycountrystore.com/gift-shops-townsend-tn
-- HikaShop version -- : 2.6.2
-- Joomla version -- : 3.5.1
-- PHP version -- : 5.6.15
-- Browser(s) name and version -- : all
-- Error-message(debug-mod must be tuned on) -- : No error - connection timeout

This issue appeared when we updated hikashop to work with Joomla 3.5.1

- I add item(s) to my cart, and continue to checkout.
- I fill out the checkout form (with either a new or previously used email address), and click 'next'
- At the next screen I am shown confirmation of the order we're preparing.
- I click finish.
- expected behavior: order is submitted and confirmed as usual
- actual behavior: the browser times-out while attempting to make the connection.

Before updating, we saw the error message that came from the Joomla 3.5.1 update after clicking the same button. Now we see nothing
Any idea what would cause this?

Thanks!!!!
[checkout config attached]

There is no php fatal, as the timeout occurs before the req hits the php. I tested my logfile with an intentional fatal error: require("foo.bar");, which logged as expected.

I can't run XDebug on the prod server - unfortunate . I did slip this piece of code into the top of several key files:

$out = fopen("/home/user/public_html/test_hika.txt", "a");
fwrite($out, __FILE__.":".__LINE__);

If it means anything to you, this is the complete flow file content. It shows the tracked files that did execute.

Got it squared away. It was an issue with the SMTP connection, and when I switch the site mailer from SMTP to PHPMail, all seems well.
The issue may be compounded by our server's csf security suite, because the workflow worked like a charm when I mirrored it to a vagrant box. step 2: I edited my hosts file to point the domain name to the IP directly, eliminating cloudflare from the equation. Running like this (on the live server - not the vagrant box - and pointing around cloudflare) I was able to let the page spin for about 5-10 minutes before it finally gave me a site-level error message with real clues.