Magical Starsign - Cart-Specific Tag Mode Egg Characters

In Magical Starsign for the NDS, there is a "Tag Mode" feature which allows players to unlock an "Egg character" feature. As the game's Instruction Booklet states:

"The egg characters you can receive are determined by the Game Card you connect to in Tag Mode. Once you receive an egg from another card, you will never receive another egg from Tag Mode with that Game Card."

While this does sound rather constrictive, it also is confusing. "'That' Game Card" could be referring to two different game cards: either the player's own, or the friend's. If this refers to the player's card, it would imply that the player can only ever gain one egg ever, which is extremely unfair and unfun. If this refers to the friend's card, this would imply that only one egg can ever be gained, hatched, and raised from that friend's card alone. This would be the first issue that needs clarification.

This then brings up another issue. Let's assume the following setup: A player has the Magical Starsign cart. Player also has an M3 DS Simply with a Magical Starsign rom. How would this player be able to simulate different carts from the rom, in order to gain multiple eggs on the legit cart?

So far, attempts have been to delete the save data file from the M3 DS Simply microSD card. However, so far the legit cart only ever gained/hatched/nurtures the same egg (for argument's sake, the "wood" egg) from the rom game. On the rom game however, different eggs are obtained by each Tag Mode entered with the legit cart.

I was hoping someone with a greater understanding of the roms would be able to shed some light on this predicament. Are the roms only ever read as the same cart, despite what save data accompanies them? Do more versions of the same rom need to be released for this purpose now? What can be made of the fact that the legit cart can give multiple eggs to the rom game which has its save data deleted, while the rom game (so far) only nurtures the same egg for the legit cart?

I hope that by our studying this problem, we may be able to gain further understanding of this phenomenon, and thus attribute some kind of identifier to this situation.