Actually the Draconian goddess actually allowed both the destruction of the Sanctum and further the death of her people.
Past that, the Triarii having forced gods away before, I don't think its impossible to believe they could do it again... Heck, the Equestrians trapped a god like being on the edge of the galaxy.

As for taking the flak for abductions, they partook in abductions and the humans have apparently never made a connection, that or they are sticking so close to the common sense doctrine they don't care
Don't expect to have abducted live Triarii though, the state generally kills them or they commit mental suicide rather than allow their capture, but then again you only need the bodies so xD
Sounds like it could be fun

Why would there be a difference between the cloning techniques? Its the stage after that which is different.
if they are put through the Triarian design of memory replacement, a complex art that relies on the machine manipulating brainwaves and imprinting pro-collective memories while removing the other memories. If you go in a anti-Collective artist you might come out a pro-collective soldier with your name reduced to a number, all your former life and personality gone, all depending on the settings. Why would it matter what fabricated the Draconians in the first place, if you are replacing someone's entire thoughts and personality what can they fo?

Though assuming Ted wasn't changed like this, his personality is very strange for a Draconian