I have never seen SQL Server take 30 minutes to compile a plan. My guess is that you do not have an issue with the plan cache being wiped out, but the index statistics being declared invalid. Just after a restore of a log, run an update stats command on a few tables in a big report, and see if performance improves.
Alternatively, it could be that the restore wipes out the data cache. Have a look at some of the disk counters to see how badly you are hitting the disks while that report runs.