I have a DMS tablespace with 11 containers, each about 4.2 GB. The last time I added a container the rebalance took about 10 hours to complete. The tablespace pagesize is 4096. Could anyone suggest methods to speed up the rebalance?

Not right off hand, but why do you have so many containers? It seems unlikely that you have enough I/O channel bandwidth on your disk controller(s) to exploit that many containers. If you just need more space (and cannot extend the existing containers) you can add a new stripe set so that no rebalancing will be necessary.

Do you think adding a new stripe set can affect read / prefetching or write performance?

Yes, it could theorectically, but sometimes necessary in 24x7 apps if that is the only way to allocate more space (if current containers cannot be enlarged). More likely to affect a data warehouse doing table scans than an OLTP system.