How do I fit a graphic into an irregular shape without clipping portions out?

I posted this in the adobe Illus. forum and got no answers so I'm not sure if it can't be done, or the forum just isn't very active. I have a vector image that I want to fit into a template. I need to distort it, so that if you fold up the template (lower right), matching the sides up, the pattern will match. Clipping masks and/or pasting into, just crop the pattern out. I tried Object-Envelope Distort, but it distorted the entire image too much. I may not be using it correctly or choosing the wrong option. Below is the pattern and template I want to fit.

Attachment 105065

I am not trying to change your design but how important is it? Is the Maltese cross shape used for packaging. If is was I would try and have the swirls growing out of the bottom and have the small leaves on the sides if it was packaging. Now just do a search for "Illustrator Swirls" you get tuts, free clip art, free brushes and free symbols/patterns all for you to use in Illy: https://www.google.co.uk/search q=illustrator+swirls+free&espv=2&biw=1440&bih=775& tbm=isch&tbo=u&source=univ&sa=X&ei=kseGVKPJEMf4UMe FgrAN&ved=0CCcQsAQ#imgdii=_

If again I was in your shoes and wanted to use your design as is then I would use a "Clipping Mask" and as the mask is still live when you apply it, it's so easy to move it around to get the majority of the design in your template shape. If I have time later today I might have a shot at it.
If you use the Google search save time, don't use just the web tab use the "images" tab and it will save you opening each search result to have a look at that particular address.