Phartiphukborlz has it.
Agreed that changing at Mordor Central would appear to make sense. Some of the Virgin services from New Street to the North West are Voyagers (diesel) rather than Pendolinos (electric) - on the Virgin Voyagers the bike space is a dangly area in the power car at one end. Unlike the Pendolinos, this is accessible from a public vestibule, so you won't need to find a member of staff on the platform to open it up.
The right-hand dangly bike space on a CrossCountry Voyager ostensibly fits two bikes. In practice it fits two bikes with drop handlebars, if they're inserted in the right order. If you come along and find someone's put a MTB or city bike in there, yours might not fit. At peak hours you may find the bike spaces occupied by passengers. Or worse, that someone's locked an unfolded Brompton in one of them. The reasonableness of train crew is extremely variable.
(If you go for the bagged bike as luggage option, there's a large general-purpose luggage space behind the dangly bike spaces in coach D.)
Book your bike on everything, it can't hurt, is necessary for Pendolinos, and gives you an extra bargaining chip if a CrossCountry guard tries to chuck some cyclists off.