Gravity & Time Travel

[JakeEscherRoels]

Ok so bear with me here...

I've been listening to Carl Sagan lectures on audiobook while at work.

Black holes gravity is so strong it bends matter, light, space... the closer you get to the event horizon, the more intensely gravity pulls. So! Someone sending messages at regular intervals who is approaching a black hole to a fixed point. The messages would be received slower and slower as the black holes gravity pulls everything in harder. This means time is moving faster for the guy approaching the black hole.
Therefore? a stupid high level of Increase Gravity would affect TIME ITSELF! (Maybe? Right?)

I realize this is both:
1. Incredibly soft science fiction
2. Stupid high levels of increased gravity and there would be cheaper ways of doing it for sure.