Your step 3 is unclear- What do you do to get the material to the vendor?
ME2O or ME2ON or MIGO? Movement type 541?
Here you usually move the stock from your own location to the vendor.
And 543 only issues from the vendor stock, not from your storage location stock.
You would even get an error message M7 021 Deficit of ....
If you have no stock in subcontracting stock type O for your vendor