Right off the bat, HR resources will generally only give the norms or median spread. On the other hand, search firms will inflate or at least pad somewhat the upper end of the spread as they need to draw the best for their databases. Probably in reality it would be somewhere in the 'tween. At the end of the day though, it would depend on what you are 'really' bringing to the table. If it is more hype than substance, well, all the titles in the world cannot help someone who is an example of the peter principle at work (I am not referring to you, but what happens in lots of instances). These guys can talk the teeth out of a chicken but when it comes to doing, well, let's just say they need their teams so that they can pinch the credit when necessary.
A lateral move at your level doesn't sound like a good idea at all if you are that senior. Especially if they are trying to shift you out of the country. According to your post, if you are being transferred by your "multi-billion" company, it should not be a real problem for them to at least equalize your salary/perks so you don't lose. This however sounds kind of fishy to me as most companies of that magnitude wouldn't do that unless they are trying to get rid of someone.