I had a look at your photo Gary.  My stern rails are 25mm x 1.5mm pipe, but are very different to yours.  I have a separate rail on each quarter which is triangulated, that is three uprights come up from different directions to meet at the top.   It is absolutely rigid and cannot flex no matter how much stress is applied. Being welded to the deck also helps. I used double sheets on the bermudian rig, one to the top of each rail, without trouble.  You could replicate this  by adding a diagonal pipe, running athwartships, from the top of the aftermost upright down to the deck, about where the bumpkin crosses the transom, but  am not sure that this is the right thing to do, since your mainsheet attachment will not go to the corner rails like my bermudian rig did.  Perhaps the most effective thing would be to brace the rail at the point where you attach the sheet blocks.  You could run a wire brace from the sheet attachment point out to the base of the stern rail on either side, or weld in struts.  Arion has bracing struts made from 12mm SS rod which work well.  I will take another, clearer, photo this morning and add it to my member album. 

My mainsheet blocks are on the pushpit. Initially, it was too flexible, so I added two diagonal bracing wires under tension, and it's been OK ever since.

I had planned to attach my mainsheet to the Pushpit but I have realised it's not going to be strong enough. So I'm looking for ideas. I could do a simple rope horse attached to the cockpit coamings or I could laminate a beam that would also attach to the coamings. The attachment point would be forward of the Pushpit.
How did you set yours up?