Just to be clear, this is PDFX-based emailing we're talking about. (As opposed to EMAILX, which can run on any platform, the PDFX version is limited to the Windows side.)
So as far as the log goes, I would suggest putting it in a SAMBA-mounted directory visible to the client PC as well as the server. (Or transferring it back to the server.)
As far as the bad address detection goes, unfortunately, this falls under the purview of the SMTP service. Some services do more analysis on target addresses than others. But as a reference, I tried both freeman123@edgemed.com and freeman123@nosuch.ca, through both my ISP (HostGator) and GMAIL, and neither one complained. I also did it with EMAILX, which is able to produce a raw log of the byte-level communication between A-Shell and the SMTP server, and it shows GMAIL (in this case clearly accepting those addresses) ...
05-Jun-19 15:10:40 [EMAIL1-joaquin-2] > RCPT TO: <freeman123@edgemed.com> [Status=35]
05-Jun-19 15:10:40 [EMAIL1-joaquin-2] > Checking for data (timer=10000ms)... [Status=1]
05-Jun-19 15:10:40 [EMAIL1-joaquin-2] > Read (flags=0)... [Status=38]
05-Jun-19 15:10:40 [EMAIL1-joaquin-2] < 250 2.1.5 OK f71sm83683itc.5 - gsmtp^M
05-Jun-19 15:10:40 [EMAIL1-joaquin-2] > Checking for data (timer=100ms)... [Status=0]
05-Jun-19 15:10:40 [EMAIL1-joaquin-2] > RCPT TO: <freeman123@nosuch.ca> [Status=33]
05-Jun-19 15:10:40 [EMAIL1-joaquin-2] > Checking for data (timer=10000ms)... [Status=1]
05-Jun-19 15:10:40 [EMAIL1-joaquin-2] > Read (flags=0)... [Status=38]
05-Jun-19 15:10:40 [EMAIL1-joaquin-2] < 250 2.1.5 OK f71sm83683itc.5 - gsmtp^M
So, I'm not sure what more you can do, other than perhaps find an SMTP server which does more testing. (I'm under the impression that that the Office365 service can at least be configured to be quite persnikitty about what it accepts.)
Note that if you're going to send a lot of emails, it might make sense to use a commercial service, since most of the free ones (and certainly GMAIL) will start to act up if they think you're abusing their hospitality.
You could also request acknowledgments, but you'd have to follow up on those manually. (In theory, that could be done in software too, but it's another project a bit outside the current envelope.)