Just by doing the circle courier mission and datacenter tag deliveries MoxNix at Merchant Monarchy raised his standings with the Amarr and Caldari factions by quite a bit.
My interest is in having good standings with all factions so derived standings and diminishing returns mean that completing storyline missions is no longer a valid option to increase faction standings for me. To confirm I completed one storyline mission.
Corporate and faction standings before completion of the mission.

Corporate and faction standings after completing the mision.

Gain: Amarr Empire +0.05, Caldari State +0.03
Loss: Minmatar Repbulic -0.07, Gallente Federation -0.03
To repair the loss I completed The Blood-Stained Stars and chose gallente gaining +0.43 standing with the Gallente Federation. Completing the amarr epic arc increased standing with the Amarr Empire by +0.57.
To compare, SoE arc consists of level 1 missions. The empire faction arcs are level 4 equivalent. All epic mission arcs can be completed every three months.

As a side note, I'll be visiting the Evesterdam event.
http://evesterdam.com/ and https://forums.eveonline.com/default.aspx?g=posts&t=357173