John,
I've joined tops and backs at thicknesses very close to the final ones and as others have said you need to take care to keep the plates flat at the join. In your position with the Wagner Safe-T-Planer I'd probably make a simple jig that would do this for you with thin plates - you need a flat base and two long beams (slightly longer than the plates being joined) that you can screw/clamp down on either side of the join. I've had the basics of such a jig in my head for a long time to use with the hhg/tenting method and one day will get around to designing/making it - two raised beams that have a sort of lever clamp mechanism that means both beams can be lowered/pressed flat quickly with a couple of levers. Slide the plates joined by tape in the tent position into the gap between the raised beams, spread the hhg and then clamp down the beams - Bob's your Uncle . . .
With hhg if the join is not flat in places you can at a push melt the glue with a hair drier and push the plates flat - the jig would be a better solution though.