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In general, a tapered pushrod should be more expensive and difficult to make, so that could be why some aren't running them.
However, making the pushrod larger diameter in the middle will make it stiffer than if it is the same smaller diameter for its entire length. It will also help the harmonics, that is true. So, it's better all around.

A smaller diameter pushrod needs to be quite thick, and it doesn't get weaker as you make the wall thickness larger. But the last 25% or so of the diameter (the part in the exact center)does very little to increase resoistance to bending, which is what you're really after. So on a 5/16" pushrod, any wall thickness over 0.117" isn't adding appreciably to the strength, just the weight.

The statement above that pushrods need to be as large a diameter as you can fit is right on. It's in the Strengths of Materials book under "columnar loading".

Some years ago, Subaru switched to overhead cams from pushrods. The design of the Subaru engine makes for extremely long pushrods. They used exactly the same camshaft profile from pushrod to OHC, and gained quite a bit of power. This was attributed to lack of pushrod flex getting the valves to open much closer to the camshaft specs.

R.

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Well stated and right on.
When Best Machine built my old 422w5 motor Chuck Millen gave me a great lecture about using as big a pushrod as will fit. With my X block we used 3/8 on intakes and 7/16 on the exhaust.
That motor was built circa 2004 and is still campaigned by the current owner. It has seen hundreds of 7500 rpm laps and never any pushrod issues, ever
Those same Manton's specced at the above diameters are still in the motor.

Regards the OP, we're it me, I wouldn't use a 5/16 pushrod in a roller with significant spring pressure. Probably would not have used that block that so limits your choices.
Might get away with it, but, IMO, that is tan extremely weak link. And weak links generally rear they're heads at some point.