Housing joint problem / oak shelf design

[Wayno]

Hi all.
I have recently built a small oak media unit ( about 80cm x 50 cm ) its split into 2 sections vertically and one of the sections I have put a stopped housing joint in order to accommodate a shelf. Mistake 1, the router jig failed to work properly ( ok I measured wrong ) and the housing joint is a couple of mm wider than the shelf thickness. I also noticed the oak shelf, which is only about 50cm wide x 40cm deep has a very slight bow in it. I'm proposing to do the following and wondered if there would be any issues.

Install an oak veneered birch ply strut, ply because there will be little or no wood movement, edged in oak so it looks solid, under each end of the shelf, which will stop about 5 cm from each side so it is not too visible, this I'm hoping will serve 2 purposes.
1) It will be fixed into the side of the cabinet and push the shelf up to the top of the housing joint and therefore cover the small gap, yes there will be a small visible gap under the shelf at each end but I think I can live with that
2) If the ply strut is screwed into the bottom of the oak shelf it will prevent further cupping. All fixings will be via elongated holes/slots to allow for movement with the grain.
I've included an image which hopefully helps explain as well.
Any issue with my proposal ? Or any other ideas?
Thanks in advance

 

[Jacob]

Would anybody notice "a slight bow"? If really bad I'd plane it out. It may be dry enough now - the good news with a bent piece of wood is that you know that it's drier than it was when straight!
Make up thickness of board to fit housing by gluing a thin strip (width = depth of housing) to each end of the board on the underside, and plane it back to fit the housing.
You could conceal it completely if you needed to, by gluing another strip along the underside of the visible front edge

 

[Woodypk]

Wayno,

If you glue a thin strip to make it fit the joint well, surely the joint itself would keep the shelf from bowing?