I think how Ibanez is spoken is relative to the place. For example, here again in Japan. In Japanese dialect "I" is pronounced as "ee" and "E" as "e" (as in egg). So if a local guy who is not familiar with musical instruments will read it as spelled in Romaji (IBANEZ), he will pronounce it as "ee-ba-nezu". But of course, when they read it in katakana アイバニーズ, "a-ee-ba-neezu", since ア is pronounced as "a" (not "ey"), イ as "ee" and ニ as "nee". Or they can even combine the "アイ" to make it sound like ""ay" so it can also be pronounced as "ay-ba-neezu" which is more likely.
Now come the mystery. How come the Japanese spelled it in Katakana as アイバニーズ? The most possible scenario is since this is a foreign word, the Japanese guys at Ibanez Japan asked somebody from the West to pronounce it. Perhaps the guy pronounced it as "ay-ba-neez". Since Katakana is written according to the sound or how the foreign word is spoken, the Japanese spelled it in Katakana as アイバニーズ. If the western guy pronounced it differently then the Katakana is also different.
The following are some other Katakana versions based on how IBANEZ is pronounced:
1. as "ay-ba-nez" = アイバネズ
2. as "ee-ba-nez" = イバネズ
3. as "ee-ba-neezu" = イバニーズ
3. as "ee-ban-yehz" = イバンニェズ
Personally, for me, the correct term should have been #4 as "Ibáñez" イバンニェズ since this is really a Spanish word.