Fixing poor detail on parapet wall

We have a flat roof with parapet wall (yes, I know).

A couple of issues have arisen that I'd like to address before they get any worse. The problems are a combination of crappy installation detail and crappy actual installation.

The first is the junction between the outer edge of the parapet wall and the EPDM-based membrane that covers the roof. The current detail is pretty poor. The parapet wall slopes inwards slightly. There's an aluminium drip trim that hangs over the outer edge, extending along the top surface towards the inner edge. The membrane is hot-welded to the top of the trim, such that it leaves about 100 mm of the trim exposed adjacent the outer edge.

One problem is that the trims are in 3 m long sections, with an expansion joint between them. The welds have failed at several points at or adjacent to the joints, presumably due to the stresses of expansion and contraction. You can see where this has happened just to the right of the joint in the above picture.

Because the top of the wall slopes towards the membrane, water tends to pool at the joint, meaning it can easily work its way under the failed sections.  

I'd like to fix this issue before it gets any worse.

I've considered laying a strip of EPDM along the outer edge (i.e., right up to and maybe even slightly overlapping the edge itself), such that it covers the join between the existing membrane and the trim. While water might still pool a little bit, it would be on top of a solid layer of EPDM rather than being along a join. I was thinking of sticking the EPDM down with some sort of permanently flexible roofing sealant.

Any thoughts about this as a plan? And if the plan looks okay, does anyone have any recommendations for specific products? I was thinking something like this, which is reasonably priced and stays quite flexible (I've used it for other stuff on the past).

Thanks as always.