I use the Shimano XT T-780 pedals, which are the predecessor of the T-8000, and get on with them well. The pedals hang with the cleat side to the rear, so a normal foot on pedal from the rear action gets the cleat side, and that using the flat side required an unusual "draw back" action. I dare say you'd get used to it easily enough if you mostly use the flat side, but I don't, so I find it a little awkward.
The main difference is that the T-8000 has grip pegs, whilst the T-780 doesn't.
I would comment that a mix of pedal/cleat types will be a bit of a nuisance - you'll have to have a separate pair of shoes for each cleat type, and pick the right cleated shoe for the bike, which will lead to either riding wet shoes, winter shoes in summer etc, or spending on duplicate pairs.
Also, if you've been riding exclusively cleats for years (mostly), flat pedals will take a bit of getting used to.
You may not be conscious of pulling up on the pedal, but it's very easy to be in the habit of a slight lift that's enough to lose contact with a flat pedal enough that the foot moves on the pedal. This may be what's happening with your plastic pedals.