Passion Pinks - Help please with weighty flowers!

I recently bought a Passion Dianthus from my local garden centre. I wanted to be able to control the conditions it is in quite carefully, so chose something I understood could be grown in the greenhouse.
I've been keeping it watered once a week, fed it once a fortnight, and generally checked on it twice a day. It had been doing well initially, not award winning results but quite good enough to wear, however it had a very bad habit of splitting the calyx every time a flower grew in size. Every flower did, so I consulted my RHS encyclopaedia and found a reference to calyx bands. I tied a small amount of wire around each blooming calyx as the book suggested.
That's where the trouble really started. The recent heat has brought several buds into flower so I've got nearly 10 flowers out. Is this too much for it? It had been struggling to hold the weight of the flowers at times already, but the addition of the band proved too much and now every shoot collapses at a node and all the flowers are facing right down to the ground. I've been tying it in and stopping a few shoots over the last month, but this hasn't helped.
This obviously isn't going to help them at all - so what can I do? Should I look to limit the number of flowers growing? Shouldn't it be in the greenhouse at all? Is there a lighter solution to stop the calyx from splitting? Any help or advice would be greatly received! Thank you for your time.

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