NPC corp to Player corp standings only count towards Jump Clones.
The only way to access higher level agents is, alas, through personal standings.
One possible piece of advice would be to get your corp mates to not engage with the agents of that NPC corp so that the corp can offer jump clone services to all corp members.
This doesn't mean not doing missions for that corp though, it means not even starting a conversation with an agent. Starting a conversation with an agent generates a standings entry on your character sheet and it is these entries that are used to calculate your corps standing.