The "three horizontal lines spaced 4 inches apart" part is what's doing the work there, not really the tape itself. Birds need about 2 inches of vertical gap max to see a barrier, so at 4 inches a small finch could still try to slip between the lines, you just got lucky with the cardinals being bigger. The reason it worked so well is that white tape shows up against the glass way better than clear stuff ever will. If you want it to look nicer, try white paracord or thin white cord stretched across instead of tape, same spacing but you barely notice it from inside.

We went through this with my oldest when he was around that age (except it was me dying to the same boss over and over, not him). What worked for us was setting a rule before I even sit down: if he wants a turn, he gets one, but he waits until I either die or hit a save point. That way nobody has the controller yanked away mid fight and nobody feels cheated. Eight seconds of him getting wrecked probably taught him a lot, but it also taught him that grabbing stuff out of your hands is fine, which is the part I'd watch. Next time pause it and tell him he can have the next run, then actually hand it over when you die. That gives him something to look forward to and keeps you from being the bad guy for taking it back. You're not wrong for letting him try, you just skipped the part where he learns to wait his turn.