I would think you could program the new remote without an original remote, but hey, I am here if you need help.
If one is making a microprocessor remote (Arduino, etc) there are 'tables' that can be used to program the signals of popular devices. Little out of the scope for this need.
You are probably aware of the remotes (supplied usually from your cable provider) that one can inset a code, they have the common codes built in also. Executive was not found as a Model or Brand in any tables I could look up, so there wasnt enough demand for them to 'Make the list'.
There is a chance that you could locate another remote code list that happened to use enough of the same codes that on/off works at least. I wouldnt put money on it, but there is a chance. Happy Hunting.
SOME Android phones have an IR emitter, and can be programmed to work as remotes. Again, not finding the codes for Executive brand/model...
I did briefly look into another system when I discovered ours was broken, but the lack of something else that fit was a big setback. Not to mention that the 'Surround sound' system speakers installed were probably mediocre for the day in 2006, and today would be considered laughable. I have a small bluetooth speaker that hooks to my phone that has better sound. Honestly, the TV I installed has better sound than the installed speakers. They are glorified hole plugs for now.
If you DO spend a lot of time watching tv/movies in the camper, this $100 subwoofer, placed anywhere near the seating area, will return MUCH depth of sound.
https://www.amazon.com/Rockville-SS8P-Under-Seat-Powered-Subwoofer/dp/B079PRCP9W/ref=asc_df_B079PRCP9W 11.4" x 8.3" x 2.8" Inches with an 8" driver.... THATS some good use of space.

Too big? These will rock your seat, and bother neighbors less.
https://www.parts-express.com/dayton-audio-bst-1-high-power-pro-tactile-bass-shaker-50-watts--295-244 Dimensions:
5.75" diameter x 2.5" high
Mounting holes 5.5625" center to center

Sorta wandered off remotes... but hey...we get topic drift here.
