Why dig at all?
The crucial question in this is how good are the existing slabs? Lift one to find out on what they are bedded.
What will kill the slabs if you place the new building on them is local point loads. The more weight you put in a single place, like the pads you propose or the individual concrete blocks the more likely you are to have problems with settlement.
If you spread the weight of the new shed over the full area of the slabs it covers, the surcharge is negligible.
Consider your 300kg lathe as 12 bags of cement. If you put those 12 bags on the existing slabs covering an area the same as that covered by the lathe, would the slabs complain? If you put the whole lathe on just one slab, that might lead to problems.
As well as the line of support in the same place as your proposed trench or line of pads, add a couple more inboard of it. If the levels work out, I would consider a U-shaped frame to form the perimeter of the new shed and then lay Roofmate directly on the slabs with your floor (constructed as a membrane - e.g. t&g chipboard) on top of that.
Another option for load spreading is the fibreglass grids you see on the railways (search GRP grating). They are very stiff, do not rot and provide good ventilation to any timber item placed on top of them. A few of those (4 x 1m squares) on the slabs and then traditional shed bearers on top of them would distribute the load into the patio.
