So time to hack:
Step 1, use a stitch picker to remove the existing sewn-on pocket.
Step 2: I grabbed a cheap and thin wallet from eBay and used Sugru to 'glue' it into place in the Lezyene wallet. I left it overnight with some packing to push out the sides of the Lezyene wallet and with a heavy weight on top to ensure the two pieces were in contact.
Step 3: A little additional Sugru around the edges to keep it neat and prevent the glue peeling.
Step 4: Finished - a couple of pockets for banknotes and slots to drop in 3 credit cards.