I ended up going the external thunderbolt SSD upgrade route, since I didn't really feel comfortable pulling apart my expensive new computer. It works great, but has obvious down sides.
* The only Thunderbolt port on my 2011 iMac is occupied.
* I can accidentally remove my system disk if I'm clumsy (and crash my system).
* I can't hide the disk and can see it if I stand beside the desk.
No biggies in other words. Very happy with the setup.
An unfortunate design flaw specifically on LaCie's part. As with FireWire before it, and SCSI before that, Thunderbolt is a daisy-chain interface. Single-port devices in such ecosystems are best considered defective.
Of course, now even Mac Pro customers don't get the space to add more storage internally.