I'll be blunt, and maybe others will disagree with me, and say that I don't think there are any impactful levers you can pull.
In my experience, Gmail frankly does not give a shit about receiving e-mail from any senders except ones that fall in one of two categories: a) very large so users will complain in large groups if receiving from them is impacted (put your Outlooks and your Yahoos and your huge residential ISPs in this category) or b) technically-savvy senders that aren't quite as large but Gmail employees routinely interact with so they're otherwise "trustworthy" (Fastmail is an example here).
I've ranted about here but I've had terrible success being smaller than a multinational ISP and sending e-mail to Gmail users. Messages will silently disappear, even though Gmail's SMTP server claims to accept the message, and the postmaster tools are less-than-useful (that might be my one suggestion, sign up for them on behalf of your domain and see if you get any reports; I didn't, 'too small'), and no amount of tinkering or asking would help.
I admit I'm just a SMB org whose business isn't sending e-mail--it's "just" a communications tool for us--so I had this option: I threw in the towel and switched to Fastmail and have had no problems since.
I had the same issue, what I found though is that DMARC reports give at least some insight into the process, but that's about all the information I've managed to get from Google.