Oh what joy!........ Problem solved!
After how long - some weeks and about 30-plus posts in this thread - I am able to mark it "SOLVED".
EasyBCD really does live up to its name. As was probably obvious, I was a little wary of using its automated repair tools in case that simply dug me into a deeper hole and left me with a computer that wouldn't boot at all.
But after the detailed descriptions of what boot screens I was seeing and what bootloaders seemed to be operating, and after extensive efforts by
SIW2 to diagnose the problem(s) by looking at the BCD stores, I tried the commands suggested by
SIW2 to edit/reconfigure the BCD store. This didn't work - as described in the various posts in this thread.
Today we seemed to have reached the end of that road, so I took
SIW2's advice - again - and hit the "Reset BCD configuration" in EasyBCD. It did its stuff.... and when it was done I followed the instructions and re-entered, within EasyBCD, entries for both Win7 and Linux Mint, the two OSs on the system.
I took a deep breath, and rebooted. Magic! After the initial "ThinkPad" screen, up came the Windows Boot Manager, and there on the list were Win7 and Mint (and below them, the usual Diagnostics option). Clicking on each of them in turn successfully booted each OS. Even better, on that Windows Boot Manager menu is also the F8 option which takes me into the Advanced Boot Options/Safe Mode etc menus.
So the laptop is now working exactly as it should, and as I had hoped and expected. I still don't know why there was "crud" in the BCD and why I kept getting that weird 'Boot or Restore' screen. All that has now gone, and as far as I can tell I have a "normal" booting and functioning system.
Just for interest, here is a screenshot (from EasyBCD) of the new "clean" rebuilt BCD configuration, for anyone interested to compare with the previous troublesome one in my post #3 two weeks ago. The peculiar 'custom' entries have gone and there are proper/familiar entries instead. I still don't know how and why the BCD was such a mess (it wasn't anything I did!). But it is all sorted now.
So I owe SIW2 a huge thankyou for his patience, tolerance and constructive suggestions (and thanks to Paul Black who dropped in and commented too). I also have to offer an apology for taking so much time and attention in seeking help with the diagnostic process (even if in the end the
bcdedit route didn't solve things). I've learned a lot.
I'm very grateful to this forum and its members. And I have increased respect for EasyBCD as a tool which helps those like me who are non-experts in this complicated field.
So this thread is marked "Solved". I'll continue to browse the forums from time to time - but I'll hope not to have to come here too often with further problems!