Wow are you serious? JC and Aegon wouldn't have Duck or the halfmaester or the GC or any of those things you just mentioned if it weren't for Illyrio and Varys arrangements. They want Aegon and JC to think they're running the show that's what controlling from the shadows is. If you honestly think JC and Aegon would be in the situation they are currently in without the help of Varys and lllyrio you seriously need to reconsider how you interpret this series. Controlling from the shadows mean you control the whole dynamics of ruling the seven kingdoms including politics not just specifically Aegon and JC battling in war. What do you think Varys was doing when he murdered Kevan Lannister just when it seemed Kevan was finally getting the realm to a relative state of peace? You should re-read the ADWD epilogue if that doesn't tell you Varys is controlling this whole thing from the shadows this conversation is hopeless.
No, running things from the shadows is not having Viserys go with the Dothraki and getting killed when what you want is for him to chill in Pentos.
It's not having Dany take the ships that are supposed to be bringing her to Pentos to Slavers Bay
It's not having Aegon abandon his Queen and attack Westeros before you're even aware that that could happen at that point.
All they've managed to do so far is provide the resources needed for Aegon's conquest and to keep Dany alive.
Varys killing Kevan is again another service being done for
Aegon (and Dany.)
Varys is risking his life for him(them).
So far they've got nothing for everything given, and they're not positioned to gain any say if he wins.
But Illyrio spent a lot of wealth and brought even greater risk to himself by aiding Viserys and Dany.
They've spent all these resources, and taken all this risk for at least 2 Targs,
It seems odd to me that they'd have a Blackfyre, who has a blood feud with the Targs raised to believe he's a Targ and have Targ pride.
His intended bride is a Targ.
His children will be named Targeryn.
For a feud that's gone so deep for so long, that just doesn't make sense to me.
additionally, it makes no sense for them to be like "Oh by the way... you're really a Blackfyre." once he sits on the throne.