Would you say that a person is more likely to use the would + infinitive form if the party is in the future?
I know that had is here in the past tense to agree with 'invited' rather than to signify a finished action but still I'd prefer to use had if the party was in the past and would if it's in the future.
I see what you're saying, but after rolling them off my tongue, I don't think I would make that distinction in real life. In real life, I'd also say '...to ensure I'd have someone..', which I think closes the difference even more.