When exactly did the andromeda initiative begin construction?

ODSY drive only seems to have one benefit over the traditional Ezo FTL drives.  Standard FTL will go about 12Ly a Day, or 4380Ly per year... 600 years will get you 2.6M Ly, a little further than the Andromeda galaxy.   The only thing stopping a tradition FTL drive making this trip is the static charge that builds up in the hull eventually killing the occupants.  Within the confines of a Galaxy, either MW or A, this doesn't present a problem as you can discharge it into a large bodies magnetosphere, any planet with an atmosphere should suffice, might even work with a large gas clouds or nebula. 

I never saw an overview of how the ODSY drive works, first think I could think of would be to use capacitors to store the charge and eject them into my wake... so it's probably not a complicated solution or even a revolutionary design, just a technology that would take up a good chunk of space and weight to fix a problem that already has an easy work around. 

Not sure why the Attican traverse specifically, trade, strategic positioning perhaps, but those would certainly explain high density around the relay systems.  I would assume that the Quarian were using FTL to search for Dextro-Amino planets, we just never see them and most of the Terran colonies are just not marked on the Galaxy map.  Note that the only system we ever see marked in the local cluster is Sol and there 12 systems within 10Ly of earth.



 Thing is, the ships already have unlimited range while within the Galaxy, a 14Ly per day drive will allow you to traverse most the galaxy, albeit slowly in a meandering path with the exception probably of  the spaces between the spiral arms where you are going to run into trouble venting your static, the Mass Relays skip you right over these impediments.   Bear in mind, getting to the Citadel in this fashion from from Sol would probably take in the region of 5-6 years, hence why civilisation clusters around the relays.  

That was, according to Vigil, one theory made by the last protheans alive on Ilos but they never had any evidence to back it.