Thanks for all the help, guys.
I should have mentioned that I am using a DLNA server to play the file over my BDP-83, not burning it to a BD or using an external USB drive. Not having to do either of those things is one of the reasons I use DLNA. I never obtained a BD burner due to the relatively high cost of media, although I have burned a BD structure to a DVD-R DL disc when working with small source files.
I should also mention that I have come across plenty of .mkv files in additional to creating several of them on my own that play fine. This is the first time in a long time I have had any trouble with a .mkv and the BDP-83.
Since it plays just fine on my other Oppo (BDP-93) I am pointing my finger at the BDP-83 because the latest firmware I have may not cover any recent changes in the H.264 spec as has happened before (and quoted here). I'm just guessing though. Because the 83 plays back something and doesn't just immediately freeze with DeEdv2.0, I do not believe it has to due with one of the old problems related to FPS. There were a couple of issues the 83 had relating to how .mkv files were encoded. One was something that was fixed in a firmware release, the other meant no longer being able to use "same as source" in HandBrake, but I may be confusing the two at this point in time.
Incidentally, I cannot use the very latest firmware update due to another known issue involving the BDP-83's "16:9 Wide/Auto" setting as is documented here:
http://www.oppodigital.com/blu-ray-bdp-83/bdp-83-firmware-55-0226.aspx
So, while I am stuck using old firmware, I do not believe any of the updates released up to this point dealt with any problem I having, they're mostly for BD disc compatibility.
I found the info on the update that addressed a very similar problem I am seeing (item#2):
http://www.oppodigital.com/blu-ray-bdp-83/bdp-83-firmware-50-0323b.aspx
As you can see, that goes all the way back to 2010.