multiuser email sending via a mail manager?

<div>I'm trying to replace the functionality of the Mailman email list manager on my old host. I need to set up a list so that a small number of authorized users (3-5) can send mail to a modest list (~350), from an email account rather than using a message composer in the list manager. It seems that phplist cannot do this - it's strictly one-way. It's not clear to me that pommo, ccmail, or webinsta can do it eather, but I can't say for sure because Softaculous won't install any of them (php version conflict). [After further reflection, I think the php version conflict error message may be false, and the real problem is running out of mysql dbs.] It appears that dada might work with its discussion plugin (http://www.inmotionhosting.com/support/edu/everything-email/302-creating-discussion-list-dada-mail), but setup looks like a bit of a hassle. I can't believe that there's really no option that replicates Mailman's discussion capability, because that's really not rocket science. What option am I missing here? Any suggestions much appreciated.</div>