OK - I was wrong. I have been re-reading Campbell-Harding and Grey's 'Celtic Inspiration for Machine Embroiderers', which seems oddly relevant to my non-Celtic tiles. They use animal motifs - and I like this insouciant griffin [?] - so I had a go.
I used polyester thread to quilt the piece and as I expected the dye transferred to the thread as well.
Moving the sheer slightly gave this ghosting. I tried the sheer over the poly satin [right way up and upside down] but decided not to add it this time.
While I had the iron out I used up the dye left on the paper on a poly sheer. I put a piece of Vilene under it becks I knew the colour would go through and I didn't want it on the ironing board.
I realise that my 200th post has come and gone without me noticing it. I definitely talk too much ...