How can I make seamless upholstered chair pads?
The simplest solution I've seen is to use short finish nails to pin a flat finishing panel to the bottom after standard upholstering to the seat bottom. The finish pins can go just around the perimeter where they may be hidden by whatever frame is supporting the seat.

For instance, if you were using cheap but sturdy MDF as the seat bottom, on top would go your padding, and the whole unit would be wrapped in the fabric and stapled or otherwise adhered to the bottom.

Then a nice piece of 1/4" hardwood plywood could be neatly fastened to the bottom, effectively hiding and paneling over all the bunching and fastening of the fabric.