I drilled 8 extra 3/8" holes in the top of my first Z's deck to increase air flow through the deck. Worked great.
An American Legion team I work with got a Toro Z62 a few years ago and we ordered Toro's striping kit with it. We ended up taking it off because it cut down on air flow too much to get good clippings disbursement. It was exactly the type you described above. I made a chain drag for my Z. It does not stripe as well as some of the roller kits but does a pretty good job. Helps break up clippings too