It's also suspicious that Varys didn't tell Dany that Ned had protested against her assassination plan. There's definitely something going on with Varys, but my guess is that he is working to put Jon on the throne. He shound know who he is and all the losses Dany incurred recently could have been arranged to make her more willing to respect and value Jon.
You may be right. If Varys can keep every one fighting and killing each other then he may clear the way for the iron throne for himself. With no heirs living for either side he could asswnd the throne which is what he and little finger want.