My current problem is that Armory shows I have spendable funds but when I spend it the network tells me it is a double spend.
Which part of the "network" tells you this? Don't conflate bc.info with Bitcoin. Your log file says the Tx was broadcasted and present in the ledger. You can also try to push the raw tx through your node to get better verbose (if broadcasting from Armory fails).
There's simply nothing in your log files that suggests the broadcasting failed.