You can always change the extension. Whether or not that works for the software you're using is easily discovered by just trying it out.
The only way to change the extension in AME is to change the format. (For example, the first 4 in your list are MPEG2 options.)
Any containering around the raw .264 video stream will screw up the embedded information.
Non-Encore Bluray authoring tools will not accept any file format that is containering that stream.
Also, if you want your bluray to be "legal" - ie be possible of passing a verification suite for pressing at a repro house - you have to export to raw .264 (thus why high end author tools won't import .m4v, mp4, mov etc).
So, not you can't just change the extension. a m4v file is a ISO media container that holds a video stream... yes m4v, mp4 and mov are all based on the same standard - and yes you can thus change the file extension and it often works but......
... in this case you need a raw h.264 stream as a file (.264).
The only thing I can think of is that you container it to MPEG-Transport Stream (MPEG-TS) with the file extension .mpg.
It has the highest chance of import but I'm not sure if it destroys the h.264 stream's ability to pass BD verification.
Note also that I've heard that the bundled H.264 encoder (made by Main Concept) does not have the mandatory "slice" support for AVC level 4.1 and higher so if you encode at that level it's already an illegal stream that you can guarantee will not play ok in every consumer blu-ray player.