I'll give advice, understandably that it might not be possible for yourself as I don't know your circumstances.
However, that sounds a lot of money which essentially you're paying for the labour - the material costs are a small percentage of that total and it's only an 8x6 shed which is just a standard small shed.
If you can, get a friend along or family who can assist. I wouldn't be told that you can't have the shed door facing the house, it just needs planning out. Looking at that picture, it looks like a new build garden. if you had the shed door facing you I'd dig a trench just to the right of where the shed will face you. You only have a 6' frontage so it's not a huge amount of material. You could build up a few sleepers up to hold the bank back with supports driven into the ground. I'd build a low level brick wall to do the job but sleepers would work. Remove the material - either green bin it or alternatively you could dig a border to get rid of some of the soil and turn over the grass to kill it. Chop up the grass sods. There's loads of videos about how to do this and use some hose to create some curves in. Drop some shrubberies in - it would look great.
Then drop some flags down where the shed sits with some cement blobs underneath and level them off. Shed bases really don't have to be over engineered unless they are carrying significant weight where a poured concrete slab would be more suitable. Remove the grass around the sides of the shed and put some weed suppressant down with some decorative gravel so you can store some bits and bobs behind it.
It would save you a lot of money. As I mentioned though, don't know your circumstances but that's a lot of coin for a shed base. Ultimately though, go with what you're happy with but I'd like to save the money!