Is there a way to lower vassal integration cost?

There is bit of misunderstanding in your sentence:

Integration it says it costs 1105 influence but the absolute maximum I can ever reach is 1k

The integration cost can go well over 1k and indeed the maximum accumulated influence limit is just 1000, but you pay for integration on monthly basis -5 points per month until you'll pay it all, not a total number all at once. So it is not as hard to offset that cost by other means like declaring rivalries, gaining support from factions, completing your ruler's mandate etc.

I was going to write here about the Vassal Acculturation, but according to wiki it has been changed - instead of reducing the integration cost by 33% now it provides Unity bonus:

The tradition Vassal Acculturation in the Domination tree causes the vassal integration cost to drop by 33%. In this case from 1105 to ca. 737, which is a reachable amount.

The influence cost doesn't really mean much as you still gain influence.

It's very difficult to actually reach zero from 1k unless you have -7 influence gain for over 100 months which integration generally is but the influence cost is maxed out at -5 per month until the cost is reached.