If yr greyhound is 44kg, it must be eating something!! Our biggest grey is 37/38kg and he's a big black muscly male who's an absolute whopper.
Ours eat raw - we get it from a local supplier but are in S Wales so can't recommend to you. Like others, we have a freezer, and feed the mince for convenience. However, we vary it with leftovers e.g. rice, pasta, roasted squash/veggies, and regular oily fish such as sardines or pilchards. Also add in occasional yogurt, plus training treats of cheese or sausage.
I think the "complete" raw diets are a very easy way into raw feeding - there are some nice ones around. There are lots of variations in how you can do it - a lot depends on budget, your access to a freezer, access to local butchers and how much time/effort you want to put in to sourcing stuff.
I honestly wouldn't say it was any messier than any other way of feeding - I defrost the blocks in the utility room and plonk them in the bowls twice a day. Can be a bit splashy as one dog in particular likes to scatter his food round his bowl before then eating it from the floor but he did that with kibble as well. We are not raw purists - because we often travel for shows/business on weekends, we will take kibble with us for those, and the dogs switch very happily between.
All our 4 are greyhounds and are doing very well on this sort of diet, with beautiful soft coats, healthy weights, good muscles, and very nice small, firm poos.
I must admit I have wimped out over tripe. The smell, especially in summer is particularly vile - it hasn't made it's way into the trolley the past couple of trips to the supplier. 