allium bulbs that split (doubled) after just one year

To any of you with large allium (globemaster/gladiator), did your bulbs split on you and are your flower heads now much smaller? Anyone have any luck getting the heads back up to size like when you first bought them? I've purchased these twice now and both times the first year they were huge and gorgeous, the second year they split and were much smaller. On the advice of Donna on this forum, I now dig up my tulips every summer and store them dry and it does prolong their lives. Maybe I should do the same with the allium, does anyone do that?

The first photo is this year, the second photo is from last year, almost the same day. I started with 9 bulbs, 3 groups of 3. I have a lot more this year.

I grow 'Globemaster', 'Gladiator' and 'Ambassador'. I planted them in Fall 2011, so this year was their second blooming in my garden. Almost all of them returned (those that did not was probably due to being crushed and compacted from having heavy tree removal equipment repeatedly driven over them during a January thaw) and almost all of them doubled. Much to my surprise, the flower heads on all of them were larger and the stems were much taller than the year before. I had always read they would decrease in size, too. I am sure my experience is not typical or normal, and I am really curious to see what happens next year.

I have very sandy soil that drains like a sieve, so I am sure that helped quite a bit. I see 'Globemaster' planted in other parts of the area where I live that have also multiplied and retained large flower heads.

I have read that you can dig them up after they die down and then replant in the fall.

Of the three, 'Globemaster' is probably my overall favorite since the blooms are very long lasting (they are sterile) and the foliage is relatively compact and does not smother perennial planting companions. 'Ambassador' is easily my favorite in terms of flowers (huge, bright dark purple-violet, sterile, extremely tall and late) but the plants are enormous and require huge amounts of space. The wide, robust foliage tends to shade out whatever is nearby.
'Gladiator' is early and pretty, but the flowers are not sterile and only stay in good condition for about 1.5 weeks before they decline and start forming seed pods.

I also grow Allium cristophii and it also returned beautifully with larger flower heads. I spread around the ripe seed heads last year and this spring found hundreds of allium seedlings. Most were shaded out long ago by surrounding perennials so it will be interesting to see how many actually live.

The only reason I have a good show of alliums is that I plant so many. They might do better if I planted a little deeper, and the Gladiator and Globemaster always come up, but I don't think they divide. The last one to bloom was actually about 6 inches in diameter or larger with a shorter stem which was probably a Giganteum. The nigrums bloomed for about two weeks and are done. I planted a large bunch of blue alliums and haven't seen one yet. Unless they are late bloomers or very small, I don't think they'll come up. I don't think I'll order those allium bulbs from American Meadows again. Considering what was planted, the return was poor. The lilies from AM have been excellent, so I don't think it is the vendor, just the variety.
Marcia