Bear in mind the problem that stops Jeff's messages getting through is that mailman 1.0 doesn't know how to handle DKIM properly. Switching to a different mailman provider won't fix that.
Does mailman 3.0 even fix this? I found it difficult to tell from their website. There's a big page on the mailman wiki that suggests they "fixed" it by simply deleting the signatures entirely, which won't work. DMARC policies state that mail must be signed and unsigned/incorrectly signed message should be discarded.
The user documentation for mailman 3 doesn't seem to exist? The links on the website are docs for 2.1, perhaps they released mailman 3 without refreshing the docs.
Google Groups may be "controversial" but if I recall correctly the main issue was the question of whether you needed a Google account or not. I'm pretty sure you can just send an email to groupname+subscribe@googlegroups.com even if you don't have a Google account. But of course this is a bizarre standard to hold mailing list software to: mailman asks users to create an account for each listserv in order to manage a subscription too!