This reply is probably too late to help you make your decision, but I would love to hear what direction you went and how you feel it is going.
I am the mother of 4 boys
my youngest was just diagnosed with LM in his neck. We did surgery, not because we chose it over schlerotherapy, but because he was misdiagnosed with a branchial cleft cycst. It was only after the surgery was performed that it was again misdiagnosed as an AVM. Just last week we went to an Interventional Radiologist who confirmed my suspicions that it was lymphatic malformation, macrocystic. The IR was really impressed with how my son looked, especially after having surgery by a dr who didn't know what he was removing. We did an ultrasound and found 3 more small lymph cysts that we will have to keep an eye on but if they do expand like the first one I will probably opt for schlerotherapy. My son did great with surgery (no downtime at all!), but from everything I've read it is rare that surgery produces such great results that it is gone with just 1 procedure. And I'd never let anyone but a specialist in this area touch my child's neck again, as our IR told us most dr. just make a mess of things and it is 10x worse after surgery. It has only been 2 1/2 months since my sons surgery, so I am keeping a close eye on him, but so far so good--I consider ourselves very lucky!