Hi there,
I think there is an inherant problem with this reaction. When undergraduates are taught about making amines, the first thing you are told is that you can't make them from alkyating a NH2...the monoalkylated nitrogen is more reactive than the unalkylated nitrogen due to the electron donating properties of the alkly chain. I would expected that you would eventually end up the the tetraalkylated amine instead of your desired monoalkayted.
Additionally, if you add to strong a base to this reaction, you will deprotonate the Boc N-H (it is rather acidic due to the electron withdrawing properties of the adjacent carbonyl). If that happens, then you are going to end up alkyating the wrong nitrogen atom.
You could potentially make the dianion (deprotonate the Boc nitrogen and the NH2) with two equivalents of BuLi and then try adding one equiv of the iodide, but I expect you will get cylisation and a mixture of products.
The main issue with this reaction is the diiodide...is it essential that you do this? If not, then I would suggest adding a few more steps into the scheme and introduce the second iodide after you have alkylated the hydrazine