Are BT still doing the free line install (not that a simultaneous provide doesn't have its own problems)?
i.e. go through the online ordering process but don't put a number in, just go with the "I want a new line" option.
Admittedly; getting a brand new line (just so you can have Infinity) is a complete waste of money (on BT's part), but if their systems are playing dumb (and nobody at their call centre is able, or willing, to override the systems) it may be the only way for you to get Infinity.
Then just cancel the old line and broadband.
OK; you'll end up with a new phone number, but you will get Infinity.
Ade
vDSL2 FTTC Infinity with BT
DL Sync 40Mbps
UL Sync 10Mbps