If one looks at The Paragon Rag music sheet one could see on how it could only be properly played on a grand piano with a sostenuto pedal. A sustained chord for two measures cannot be done properly on an upright piano because it has no sustenuto pedal to begin with for that time period. Only a select few very expensive ones with tricky mechanisms have a sostenuto pedal to make the piano piece work as written (Note: the sostenuto or middle pedal on most grands 5'5" or larger. One plays a chord, then press the sostenuto pedal down. Only those dampers will be held while the others will continue to mute after the key is released, allowing only the held notes to sustain). In any case, this would strongly suggests that Paragon Rag at the very least was composed with a grand piano in mind, and therefore possibly composed when he had access to one. Other Joplin pieces such as Bethena and Binks Waltz might have benefited from a grand piano as opposed to a vertical upright piano. Looking and listening to a Bethena or Binks Waltz music would more than likely call out for a tone befitting of a grand piano than not. Scott Joplin may have used a grand piano at John Stark's store (music publisher on many of Scott Joplin’s ragtime composed pieces including the well-known and famous The Entertainer and Maple Leaf Rag songs), at a nearby social club or with some of his friends who had pianos. Knowing some of the history helps with learning on how to play, namely, Scott Joplin's ragtime.
With thanks to "Perfessor Bill" who is a ragtime genius helped shed some light on the ragtime question.
