But now I’m getting bounces just because the reverse DNS doesn’t match the name my mail server uses. There is no security in this, any spammer can program their mail server to use the reverse DNS name of the system they have taken over. But I guess some don’t, so another wall is thrown up, and those people won’t get invites to my parties.

Doesn't matter what they program the name to show. Servers that require rDNS also do a forward lookup on the domain name and match the IP address. So this only applies to a computer that's been taken over. At that point, other rules will take over like connections per IP and such.

This one is really stupid because it’s quite common for a single machine to have many names and serve many domains. However, it can only have one reverse-dns for each IP address it has. And that screws these mailers.

1) A machine only has one name it uses in the HELO command, the actual machine name. That is the one that must have rDNS.

2) You can have multiple reverse DNS for a single IP:

; <<>> DiG 9.2.1 <<>> -x 206.125.209.104
;; global options: printcmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 16414
;; flags: qr rd ra; QUERY: 1, ANSWER: 3, AUTHORITY: 1, ADDITIONAL: 0

;; QUESTION SECTION:
;104.209.125.206.in-addr.arpa. IN PTR

;; ANSWER SECTION:
104.209.125.206.in-addr.arpa. 86400 IN PTR ecc.net.in.
104.209.125.206.in-addr.arpa. 86400 IN PTR mistral.co.in.
104.209.125.206.in-addr.arpa. 86400 IN PTR mistralsolutions.com.