Thank you for the setup explanation, Branden. When you say the Roku, of course, plugs into the TV, is that with composite video (yellow cable) and audio (red and white)?
From writing out what seem to be your setup, I did see you saying you had a splitter to feed either the FIOS OR the DVD Player to the TV.
Then I see you say you had BOTH the ROku and the DVR feeding into the TV.
I don't have a DVR but I do have analog cable and a number of DVDRecorder and VCRs attached in addition to my Roku.
It might be as simple as getting an audio/video selector switcher that has 3 inputs (FIOS, DVD player, Roku plugged into its composite connections) and 1 output that goes to the TV. Then you would have the choice of sending either the FIOS, the DVD player, OR the Roku to the TV. If you are watching one of these, you do not need the others having an open line to the TV at the same time. A matter of pushing a button corresponding to the right unit that you want to send to the TV. Maybe something like this.
Actually I use such a switch with 6 inputs and 2 outputs that connect my various units to the TV. My cable is on a splitter and goes directly to the TV as well as to each recorder but my recorders all are connected to the TV itself with composite video (or S-video) and RCA audio to my switcher and the switcher out to the TV. When I want to watch the Roku I simply push in the button that sends the Roku's output to my TV's audio/video jacks and watch it on the Audio-Video Input Selection on the TV. On my old 1995 RCA TV I watch it on a Channel 00, which is a special channel that particular TV had that shows you anything connected to its back a/v input jacks. It still amazes me how futuristic that 1995 set is as I can still use it with all the modern players. It has composite and S-video input jacks. My second output goes to a 32" LCD HDTV so I have a combination of both old and new TVs..until my 1995 goes kaput.
Does any of this sound like something you might try? I have written out a drawing of what you described as your setup. Maybe something else will dawn on me to suggest or getting into more exact your setup like... I assume your splitter is 1 GHz or higher,etc.
Talk to you when you get back.
Original Roku 1, called N1000,bought 2008 (2014 still works perfectly)
2014 new owner of Roku 3500 (HDMI) streaming stick