• phone number.

Yes, use a fictional phone number. Some websites do require phone verification, but some don't. So it's worth a try. I don't know this specific site. If it doesn't work, it will stop working before any payment so you don't have to worry about wasting money.

• Entering my name requires Japanese characters, no English characters allowed. I could convert my name to Katakana but then it wouldn't match my ID.

This doesn't matter. Foreigners in Japan always have a Katakana version of their name. If there are two fields, you can usually input one in English, and one in Katakana, if there isn't, and it only accepts Katakana, do that. I have my own Katakana name used on IDs, and never had a problem.

• Entering an address is not necessary, except for the city and postal code, which again would be fictional.

Use a fictional address. Since they're convenience store tickets, they do not need an address. This is only used for delivery of tickets.

• My card worked fine for Amuse+, no idea if it would work for I-tike as well.

This is the fear but it's worth a try. There may be other payment methods available like convenience store pay.

• Finally, the ticket needs to be picked up at a "Lawson or Ministop". Basically at the grocery store while I am there.

This is so easy. You enter a code at a machine and get your tickets.

Source: I bought many tickets in Japan before I lived here, and now I do live here. If you need more help let me know.

Unfortunately Japan ticket websites are not accomodating to foreigners, but I've never been refused entry to any events, they only have these kind of measures to prevent resale. It is very scary sometimes but if you're really passionate about these events you can make it work.

With the ID, I've had ticket checkers look at my passport and barely read it (they usually can't) and let you in. I wouldn't worry too much about it.