There are two tools that might make the job a whole lot easier:

A stirrup hoe:

using this tool it is possible to reach under the grassroots to the height of the stirrup cutting the roots.  This will make rows of turf that are much easier to pick-up and replant or toss in the compost pile.  The cutting edges have to be kept sharp, that's the downside.  It is possible to find them with a wheel on the front to make it easier to use.  

Another is:

 

This tool is about 2 feet wide with 5 foot handles to either side.  Simply step on the foot bar and lever back to turn the soil.  Two things:

1.  The handles should be made of wood, not metal.  

2.  Make sure the tines are slightly curved, as shown.  

There are plenty of fakes on the market.  Get one based on the original design - as shown - otherwise it's a waste of money.  How useful it will be depends on how much your soil is compacted.

QUADS!!! are your frrrrriends.
Before you know it, you'll be fit for Gstaad black diamond, in season, of course.

Diversity is the key to economic and political evolution.

I would recommend the stirrup hoe as well. I find it very useful for "de-turfing" and clearing away crabgrass and weeds. Could I suggest a rolling lawn seat or a home-made stool as an aid. I can work all day if I can do a significant part while seated. I have a stool I made from scrap lumber that is about 16" high, with a 3/4" ply seat and legs formed from 2x4s into the shape of two "U"s. It was put together from deck screws and has the flat sides of the "U"s down so that it does not sink into the dirt. I just toss it onto my wheelbarrow or lawn tractor trailer.

My daffodils are in full bloom and the forscythia is starting to bud out. The red-buds can't be far behind. We just finished a week of temperatures in the 10C-15C range and I have spent some time out doors. This has been limited by an untimely occurrence of what felt like the beginnings of an ulcer. Instead of anti-biotics for H. pylori the Dr. gave me some super anti-acids which, unfortunately have the side effects of making me feel like I am on speed, which I have always hated. While I loved weed and wine, I never knowingly did weed, whits and wine, though I loved the song by Lowell George. Things seem to be coming under control, but I am taking it easier than I otherwise would be.

As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."