We use izettle in the shop and it is essentially a clean and reliable easy to use EPOS solution - all we need is the ability to link inventory / product title / sales by SKU to this channel ideally so we can quickly add to izettle when listing new products and also register the sales and inventory changes that are made in the shop back to Linnworks. iZettle already use a SKU system of sorts, but allocate their own SKU.
We haven't developed an integration for iZettle, but we have our own EPOS solution integrated with Linnworks called LinnPOS-
This system supports all the functionality that you have highlighted and more.
We are happy to provide a demo if you are interested.
T: +44(0)207 096 5012