Hi Lada,
It's expected that you get multiple transcripts for each cluster-ID. This is because you can have multiple isoforms per gene (biology) or because the assembler has generated some redundancy (technical). Either way, the reads which map to these should be aggregated to clusters, which is what corset does. There should be a file generated by corset which gives you the counts for each cluster by sample for DGE analysis.
To annotate each cluster to a gene there are a number of approaches. For example you can take the longest transcript as a representative and use blast2go. You can also use lace to create a superTranscript representation for each cluster. This can be useful for differential transcript usage analysis (DTU), visualising mapped reads and SNP calling. If you want to do DTU analysis, the -D parameter need to be set high as you mention. However it's not clear to me why this would make corset run so slowly.
I think if you are only interested in DGE analysis, using the original corset results is fine. The number of transcritps/cluster you have sounds about right from my experience. Best of luck with your analysis.
Cheers,
Nadia.