Doing more research into this I’ve found something which hasn’t been mentioned here before: the E3 Game & Watch “Manhole” card is not the same as the Manhole card featured in this set. This set has the same Manhole card which was sold alongside the e-Reader at launch, which further leads me to believe that these cards had nothing to do with the E3 convention.
The website which had the mounted e-Reader image I used in my previous post linked to a different website, Pixelboy’s e-Reader Zone, which was last updated in 2004: erzone.caitsith2.net/plain.htm. You’ll notice that it lists two different Manhole cards: 00-A000 and 02-A001. For the sake of this forum post, I’ve rehosted these images on Imgur:
00-A000
This was the card given out at the E3 event and is also the same as the “For Position Only” card, albeit without the Pokémon back and without the FPO text:

02-A001
This card was sold with the e-Reader device. To quote the website: “This e-Card is sold together with the e-Reader, as part of the “Sample Pack 5 Card Set”.”:

Back to the topic at hand, this website also contains the entries for several other relevant cards.
- 00029 - Pichu (E3 2002 Promo - May 2002)
- 00030 - Hoppip (E3 2002 Promo - May 2002)
- 00058 - Pichu (Expedition Base Set - September 2002)
- 00112 - Hoppip (Expedition Base Set - September 2002)
- 01079 - Hoppip (Sample set - August 2002)
- 01087 - Pichu (Sample set - August 2002)
Unfortunately the website is coded using a frameset, so I can’t link directly to them. From the images shared earlier in this thread, it looks like these hole-punched cards use the same e-Reader code as the Expedition Base Set launch and not the ones from the E3 convention.