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Reonainoue thanks for the explanation. I now understand you want to put the tackle box in the bottom of the RPS opening to the back. I thought you meant the back that you lean against hence I didn't understand.
Now in answer to your original question, yes as you indicated they use it for tank storage too so you could cut out the back and slide in the beautiful tackle drawer system you showed.
It probably will be fine especially when sitting while facing forward. I as an engineer like to slightly over-design when not doing complete stress analysis and therefore would build and internal reverse "U" wood frame supporting the back facing edge of the bottom seat.
Slide in the drawer system and yes use a Starboard cover. Are you keeping the OEM 2 drawers?