The little dot 1+ is a hybrid tube amp I believe, and the Schiit asgard is ss class A.
The HD600's do sound nice out of the Asgard apparently, Haven't heard much about the Little Dot 1+ with the HD600s
It's just cheap, I can get hold of it locally in New Zealand, and I have read some good things about it.
The K240's are on the list too, and they are around half the price of the K702s and Hd600s
Save the wallet a little and I say go with the K240 and which ever amp you can get cheaper.
The HD280 were not lacking to my ear, though compared to typical consumer headphones with a bass hump they might sound that way. For mixing/producing you almost want to veer towards the leaner side anyways. For casual listening you go to the emphasized side.