Site Can't Be Reached - Connection Was Reset for all SSL sites after LetsEncrypt renewal

Looks OK, anyway, try a different cipher and protocol just to be sure:

ssl_ciphers EECDH+AES128:RSA+AES128:EECDH+AES256:RSA+AES256:EECDH+3DES:RSA+3DES:!MD5;

The following command shows that you have no cipher and no protocol:

sudo openssl s_client -connect network1.outsmarthosting.com:443 -showcerts
CONNECTED(00000003)
write:errno=104
---
no peer certificate available
---
No client certificate CA names sent
---
SSL handshake has read 0 bytes and written 305 bytes
---
New, (NONE), Cipher is (NONE)
Secure Renegotiation IS NOT supported
Compression: NONE
Expansion: NONE
No ALPN negotiated
SSL-Session:
    Protocol  : TLSv1.2
    Cipher    : 0000
    Session-ID: 
    Session-ID-ctx: 
    Master-Key: 
    Key-Arg   : None
    PSK identity: None
    PSK identity hint: None
    SRP username: None
    Start Time: 1470575917
    Timeout   : 300 (sec)
    Verify return code: 0 (ok)
---

And see if it helps.

I also think something went wrong during the certificate renewal process.

Try this:

sudo apt-get update
sudo apt-get upgrade
service nginx stop
/opt/letsencrypt/letsencrypt-auto renew 
service nginx start