We have the same issues.
In some cases we've been able to combine reports so they come up in a single report/pdf.
To do this you really need to have each individual report in a sub-report, ie 1-layer reports. This is where it gets difficult, and if the reports are reasonably long, it's not a good solution for the users either.
FWIW, where you have 2-layer reports, you need to somehow collate the subreport info in a prior subreport (run in a prior section) and pass the info through shared variables, often arrays or similar. Messy, and it requires a lot of skill and experience.
A cleaner solution is to run everything from a custom app, ie make the reports and send them in an email. I guess this means you could bypass Logicity or only use it for the report generation.
However, this sort of solution is looking more and more attactive to me, as the addressee base seems to be changing a bit too quickly for manual management. I already generate the rrd files from Access, to it's not too much more effort to generate the rrd file(s), run them and send out the emails. One schedule, multiple outputs.
Andrew