damn I just spent about an hour writing a reply and my connection dropped just before send - so here goes attempt no 2.
the short lengths arent really much of a problem - you can visualise it like this - the current beams are sagging evenly throughout their length, any added fillets will in effect be rigid sections that resist sagging except where they join - so the span begins to act as a series of hinged panels - now assuming the panels are firmly fixed to the existing beam the stress occurs at the joins (over a very short distance perhaps 2mm) this has the effect of making it more like a shear stress, which wood handles very well.
having said that, yes it would be nice to fix them all together - but adding an overlap would be doing a job that the existing beam could do just as well. It would be effort best spent finding the perfect fixing.
mechanical fixings (nails, bolts) tend to weaken beams where they peirce.
that is why you should only ever bolt a beam at its (horizontal) dead centre - which is not subject to any stress. the problem here is that you need to fix your fillets to the beam at the top and bottom or you arent adding ay strength.
I would suggest that you use one of the new polyurethane wood glues. they are incredibly strong and longlasting, being developed for boatbuilding. they foam slightly as they set so that you get a constant join even where the wood is slightly out of contact. unlike pva based adhesives - they can be got in a variety of setting times and use the moisture in the wood to speed the setting - they also set underwater for what its worth.
the only fixings i would use would be some nails as tacks to hold it in situ (along the centres) and lots of clamps.
another option is that you can buy constructed beams (my local builder merchant Travis Perkins stocks them) - in an I section with pine top and base joined with a thin fillet - they are incredibly light and dont cost too much.
as for what sort of ply - well the best quality that you can get is birch ply, but i think it would be overkill to use it - shutterply is prone to having breaks in the laminate. so perhaps a marine ply would be alright. although I have heard it said that the best board for dimensional stability along its plane is stirling board - that stuff that is made from very large chips pressed into a board.
this is what the comercial constructed beams are made from too.
finally a link to the glue I mentioned above - there are lots of different manufacturers but Bison where the first to introduce it in the uk - I just cant remember the name of the one I use so the link is to bison.
PU MAX TIMBER THIXOTROPIC
PU MAX TIMBER LIQUID
ther are others including bison risorcin but i cant find spec on the website.
here