Hi Tim,
 
Most of my inner covers are homemade, and very simple.  I use 3/8"
exterior-grade plywood, and nail/glue a 3/8" rim around the upper surface.
(The lower surface is just flat.)  Then I drill a 2" diameter hole in the
center, for feeding, venting, or whatever.
 
I have never had a problem with de-laminating.  I do put one coat of latex
paint around the edges, but I don't think that would make much difference.
 
Yes, I have had the same problem with old, thin inner covers tearing apart
and leaving wide splinters stuck to the top bars!  It is a pain.  Also, the
cheap "masonite" inner covers sometimes swell up with moisture and often
warp -- you can't win!
 
Let me suggest that (perhaps) you are having the problem because there is
inadequate bee-space above your top-bars.  No fault of your own, just some
manufacturers don't leave enough bee-space above the frames like they are
*supposed* to.  Try this, anyway:
 
Tack a thin rim to the undersides of the inner covers.  That is, maybe a
scant 1/4" rim.  I have seen this done on some homemade inner covers.  That
may be all you need.  (On the other hand, I have seen some inners that had
3/8-1/2" rim above *and* below, and never could figure that out.  Always
ended up with lots of burr comb on the top bars.  When it's full of honey
you have a nice mess)
 
Let me know how you make out.  If you can get a good 1/4-3/8" clearance
between the inner cover surface and the top bars themselves, it should do
away with the trouble.  Good luck...
 
Best wishes,
 
Joel Govostes
Freeville, NY