if my memory serves me well and this may have changed since i left in march but the maximum time for the checker to reflect details is 52 days after day 52 their is an escalation process for the isp's to follow with Openreach.

I gave in and ordered the phone line. Now I have the pleasure of waiting until the 25th for an engineer to be available to hook that up before I'll know

Once the engineer arives in your premises and before he /she carries out any work ask the question they might know the answer if the answer is no cancel the eng then cancel the order. OFC this only applies if you see an actual eng as the prefit and prewire may have been carried out as its a new build and as such you may only need connecting at the cab/exchange and wont see an eng just a phone call telling you its all done.

But I still need a BT line either way to get ADSL2+ if I can't get Infinity, surely?

you need a "telephone line" however it does not have to be a BT Retail line may still be an Openreach installed lione but not a BT Retail line SKY and Post office do line installs alos think Orange may do as well and they may be cheaper to "install" then BT retail and may alos be cheaper line rental as well. Remember BT Retail is a Teleocoms provider and an ISP BT Openreach provide and maintain the network for all providers who wish to use the service on an equal acess