For anyone else that may have a problem with creating a site-to-site VPN where one has a dynamic IP address, the last part of the puzzle is enabling Source NAT on the dynamic side for clients being assigned IP addresses (in my case, another switch is handling out DHCP addresses, not the SRX 110). Once I enabled this and tinkered with it a bit, everything started working just fine.
Also if your sites have a decent amount of latency between them, make sure to run "set security flow tcp-mss ipsec-vpn mss 1350" and set the MTU of the st0.0 interface (or your actual tunnel) to 1500 on both devices. Otherwise the speeds are painfully slow which will result in a timeout.
Hopefully this is useful to anyone else out there trying to setup a site-to-site VPN where one end is dynamic with another router handing our DHCP addresses.
Guess these old SRX units still have some use after all!