I have had 3 cakes of yarn sitting here for time immemorial, and I want to make them up into a bag and felt it.

I want the bag to look like this:

I’m figuring out a pattern that uses pie-wedging to get the semi-circle shape. I will slip a stitch at the end of every other row, then pick these up and knit them as part of a single, circular piece that will be both the strap and the base of the bag. I will knit the strap and bottom of the bag in the round, as a single section of garter-stitch. I want to avoid sewing anything because firstly, I hate sewing, and secondly, I think that if everything is knit together, it makes for industrial strength felt when you then go on to felt it. My bags need to be industrially strong as I have a tendency to fill them to capacity. My brother once took a bag from me and immediately exclaimed ‘have you got lead in this?’ My plan works beautifully, except that I have no idea how to graft the second semicircle onto the bottom/strap band. Any ideas?