From Tier 4 to Tier 2 and then EEA Residence Card?

Hi,

I'm a EEA citizen and my wife currently holds a Tier 4 Visa. I'm now exercising Treaty Rights in the UK (as a jobseeker) and I want to apply for a residence card for my wife. She just got a job offer from a company which is willing to temporarily sponsor her while she gets the residence card. Since the processing time of the residence card, according to the UKBA, is up to 6 months, we were wondering if we better apply for the Tier 2 Visa and once she gets it we apply for the residence card. Does it make sense? Should we apply to the residence card right away instead?

Thanks in advance for your help.