dividing Tulbaghia violaceae

Does anyone have experience in managing this perennial favorite?  Some of the clumps I have are outgrowing the space I have them in, and I would like to shrink them back a bit.  Is it okay just to remove the bulblets around the outside, or do I need to dig up the whole clump and replant the newer outer bulbs in the space?  Do the central bulblets get pithy and die like in some other bulbous plants? 
 
Also, I am planning to move some Munstead lavenders to a place where they might show to better advantage.  Do they transplant well, or am I wasting my time?
 
Thanks in advance for the advice.
 
Karrie Reid
Folsom Foothill Gardener
Sunset Zone 9, USDA Zone 9
 
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