Wishing you lots of luck with your cutting!
If you take clear pics of it's bloom and overall growth habit and start a new thread on the main rose forum maybe someone can identify it for you.

Here is a link that might be useful: Main rose forum

The last bloom looks like Iceberg to me.

Here's a shot of Iceberg to compare it to:

Sysonby, I believe you may be right; it does look like iceberg. I was hoping it was something more unusual!
I did not post this in the discussion forum because I thought it would annoy people there; you already have a "name that rose" gallery. I don't think you get as many responses in the galleries, though.
Thanks for your help!
Rooty