I have BERNINA machines and they sew sidewise. Somehow, I think you are asking a double question. To sew sidewise, just lower the feed dogs and stitch away-just like you do to free motion quilt because that is what you are doing. Some quilting frames, such as the John Flynn model, are intended to use in the perpendicular position-but you are FMQing with the feed dogs down.
Now, if you question is, can I sit and sew with the faceplate of the machine facing me as I sew from side to side, you need a different machine structure-one that I am not familiar with. Are you asking if there is a machine available that sews from this perpendicular position with feed dogs up and measured stitching?
I will look forward to other comments because this is an interesting question.