Actually be better to work on the Faction instead of the Corp standings. With high Faction standings, you’ll have access to all high level Agents in every Corp within that Faction.
For more info on quickly gaining Faction standings, check out ‘The Plan’…
A few people have completed similar goals and have reported their progress in the forums, hopefully a google search for ‘Eve Online Forums - Faction Standings’ will provide a good list.
One thing I can tell you from experience is that doing a goal like that is definitely long term…