My question is, of the options listed, who's got the best deliverability to Gmail users? As a small mail server operator, that's always been my biggest challenge.
Check that here: http://whatismyipaddress.com/blacklist-check
However, deliverability has become really difficult. It seems during the ten years since I last ran my own e-mail, it has become an oligopoly. I have SPF, DKIM, DMARC and reverse DNS, my IP is not on any blacklists, and still my e-mail ends up spam listed in both Gmail and Hotmail. It seems to be getting a worse treatment by Hotmail but it's hard to say due to the small volume.
It is getting better but slowly, it seems.
I had some issues with Gmail but adding rDNS IPv6 and enlisting into DMARC fixed it.
I sent about 125k per week, 80% gmail, no serious issues (I would known cause users pay for email's content).
mxtoolbox.com
Edit: Looks like you can, but Google says it's "not recommended." Also, you need to be a paying Apps member to use the service from what I can tell. Not sure if you can if you aren't a paying member.
Scroll down to Step 6, where it shows "Any addresses (not recommended)"
Apparently, it works, but with some notable caveats, like: "If the envelope sender is not in one of your domains, the system changes the envelope sender from user@[domain you don't own] to postmaster@[your domain]"
The issue would likely be the limit on messages per day. Google spells this out for paying Apps members (https://support.google.com/a/answer/2956491#sendinglimitsfor..., see "Limits Per Customer")
They don't say what the limit is if you're using SMTP relay as a regular gmail user. I suspect it's much lower.
They respond quickly.