With this site I wanted players to be able to play with micro amounts, have instant payouts and not worry about fees. Usually that would require a third party service like coinpot, which doesn't allow payments last time I checked. Even so, they charge fees and are centralized. For this particular concept NANO happened to be a good fit. Because transactions are free and fast, I can automatically payout users when they leave the game. Most transactions are fully confirmed within a few seconds.
I understand your points and find the thought processes behind them very good, but I also agree with @adaseb.
Very few players will own NANO, once they see that there is a need for Nano on the site, they will most likely turn their back on it. Nano is simply not very common, although it is very good for your game.
Could you possibly connect different coins directly? For coins like BTC, where transactions take a long time, you could simply display the transaction ID instead of the instant wallet transfer with a hint that players should rather use Nano if they want to see the coins in the wallet immediately. This would be a soft-force to get players to switch to Nano, but you don't scare them away immediately. Would that be a possibility?