Some good news.
I installed the latest update on my Synology NAS and I no longer have the issue with delayed play.
My largest file, 65GB, plays under 3 seconds which includes display rate switching.
I already had the latest DSM version running on my Synology 1513+ and was still having the long delay issues, but I updated my SMB settings to match the ones in daneel3001’s screenshot and now everything is almost instantaneous.
I also had long-delay issues skipping forward/backward during playback and those have been resolved as well.
As of this post, I’m running DSM 6.2.2-24922 Update 2, PMS 1.14.1.5488, and Shield TV 7.2.3.