To Till or Not To Till

That is the question!  I am seriously wondering about the effect of tilling on the structure of the soil.  In the late fall, I added 40 large garbage bags of dry leaves to the garden, and in January, we spread 3 months worth of manured coop straw from 40 chickens.  Again, in March, we once again mucked out the coop and spread out the contents onto the garden soil.  All in all, it was a decent amount of amending.  The photo below shows about 1/3 of our garden and you can see the straw sitting on top.  Due to the fact that we literally had to throw/pitchfork it over to the garden from the coop area (as there was 5' feet of snow on top of it when we put the straw on) it didn't quite make it all the way to the back area.  We'll have to get out there and spread it around a bit very soon.

Nothing had been dug in - the leaves and straw were all simply spread out or thrown on top of the garden.  Add 5' of snow, and a long cold winter, and you have a recipe for some serious decomposition underneath.  Now that things have defrosted, and the snow has finally melted, we are left with some spectacularly loamy looking soil (albeit a little soggy still).   As a tentative test, I inserted a pitchfork into it and was shocked to discover how little resistance there was.  The fork slid in like a hot knife into butter.  Hmmmm...  maybe this layering really does work.  I've not seen much in the way of worms just yet, perhaps they are still too deep to see.  They won't surface until the soil warms up and thaws out deeper down.  The picture below shows what the soil look like underneath the straw.

So the big question remains...  do we till the garden?  I know that shallow digging will add some air into the soil which is needed - the surface looks very compacted and "sealed" if such a description is fitting for soil...  with all the moisture and the weight of the snow, surely things must be a little compressed at the surface.  I'm confident that a little shallow digging would really be of benefit.  This next picture shows the state of the surface of the soil where there is no straw/manure on top ~ it's kind of compacted looking and it really needs some air, I think.

Enter into the equation a husband with a deep, burning manly desire to get on the little red tractor and get things stirred up!  He has been looking forward to tilling the garden for months and months.  It gives him great satisfaction to do so and as I've seen, that little tractor and it's rear tiller can REALLY get things aerated and fluffy.  Last year, if you stepped on the soil after it was tilled, you could sink down 6" into the garden!

So, the questions remains...  do we shallow till or not?   Our garden is very large and turning it over by hand would take days and days (that I don't have).  Any advice about soil structure is greatly appreciated!