Gee, I don't know how to answer you. This project - I would just put the 2 pieces together, bobby-pin the edges together. Then use a whip-stitch to join. Likely I'd do the whip-stitches pretty close together and of course use the same yarn as you used on your shawl.
Through use, the whip-stitches tend to flatten out. And they hold together nicely, in my experience.
Sewing side-to-top? You will never get an invisible join... simply because the stitches on the side face sideways and the stitches on the top face up and down.
Sounds like this is just the way your pattern is intended to look. So go with it - don't fight it. If you don't like the result, keep it to wear around the house and find a pattern that you find more appealing to make up instead.
Here's a hint: if you are making a shawl, try creating your own circular needles by using a honking-long length of weedeater nylon thread/filament and two wooden needle tips (6-7" or more) that you drill out the centers and glue the weedeater line into each. This way you can easily fit a whole long shawl on your needles and not need to piece together the results.
I think there are videos on the Net that show you how to make your 4-5' long circulars. Not hard, really!
Hope this helps,