I don't think lump sum deals should be removed. There are many legitimate uses for lump sum deals and without them, trading would be even more boring and one-dimensional than it already is. We need more trading options, not less.
I never hated that feature. It presented you with an interesting strategic choice - should you cheat a civ for short term gain and screw up your long term reputation and limit your future diplomatic options? Perhaps its implementation in Civ III was somewhat flawed, but the concept behind it is realistic and makes sense. Some simple ways to improve it would be:
1) Only civs that have made contact with the AI you cheated would hear of your duplicity (and while we are at it, please bring back the "bring X civ in contact with Y civ" trading option, which would provide useful strategic value).
2) Civs would only flat out refuse treaties of a similar nature with you. So, if you broke a defensive pact, civs would become very reluctant to sign defensive pacts with you. If you broke a per-turn deal, civs would be reluctant to accept your per-turn offers. They should still be willing to accept other deals like lump sum gold, open borders or research agreements.
3) Civ distrust of you should slowly fade with time. Emphasis on "slowly" to make sure that you stay in the diplomatic doghouse for a hundred turns or so.
I agree with all of this.
The exploit isn't that you can be a duplicitous jerk in the game. That is in fact how many leaders/civs were. It's that there are no consequences.
CivIII's consequences may have been too strict, but that doesn't make the entire concept wrong.
You should certainly be able to screw over another Civ in this way at the expense of your reputation.