Earlier quoted context omitted.
I had similar problems. On top of that, I forward my email through my own server to GMail (so I control the domain, but can use the GMail ecosystem as UX), and this was posing problems because GMail would greylist my server quite a bit for sending in too much spam. I now run rspamd on my own server, which does a pretty great job. With properly training the bayes filters it has, I now receive on the order of 3 spam me…
Actually, that's the exact situation I'm in as well. So to clarify, the spam that gets through rspamd lands in gmail's spam folder, so you still need to manually check that, but all the obviously-spam stuff has been cut out before it ever got to gmail (solving both your problems). Sounds like exactly what I asked for! Interesting your mention about being grey-listed too. How did you determine that happened? Presumabl…
Of course, rspamd lets you tweak the thresholds for these levels. For example, after a while I lowered the threshold for "spam", increasing the amount of stuff that gets discarded by rspamd, because I noticed that rspamd was doing a pretty good job of scoring, and the false positives I was seeing had a lower score anyway.
I'm actually not sure grey-listing is the correct term, but I noticed in my server's MTA log that Google was rate limiting me a lot because my server was sending through significant amounts of email. This was also noticeable sometimes because it would take quite some time for email to get through, which I found annoying.
Yes, you probably want to run SRS as well, otherwise GMail will be unable to correctly understand your headers. However, this effectively puts your server on the hook for any email forwarded; this is why I don't think you want to go there without also putting some kind of spam filter in place, otherwise I assume your server's reputation will deteriorate.