I like the fictional descriptions you've added to all of your Network options, Hidersine. That's one of the things that I liked about Dweird's original writeup: all of it provides fictional hooks, both in terms of leverage and trouble.
However, I don't think we should discard the dice mechanic just because other playbooks use it. Followers and Wealth are pretty similar, but they have very different feels because the Hocus is different from the Hardholder and they could both totally be in the same game without it being a problem.
The other reason the "payoff/payoff and some trouble/all the trouble" moves are great is because of that line at the end of how you have the Network written: If a component of your network becomes contested... Contested says who? The MC is supposed to throw fuckery your way, but as both MC and player I like the dice to come in to help disclaim decision making.
For example: The first session opens with Key showing up at your door, needing you to cover up her indiscretions with a dead boy or a live mutant. Oh, and it's also Jonathan's favorite boy/mutant, and your position with him is now in jeopardy. That sounds like a great scene! But as the MC, I'd be reluctant to drop that much hammer and as a player, I might feel put upon if that much hammer was dropped on me – unless a miss was rolled on Businessman, fair and square.
That being said, I think I'd put in on all of the gig-options from my list stuff like "as long as you hide their little indiscretions (not so little), +Technical work" and so on. And then have Businessman have something like "instead of or in addition to catastrophe on a gig, the MC may have one of your contacts come to you with (as) a problem." I'd probably also change the Upkeep-to-trouble mechanic to be "For every Barter less than your upkeep you pay, gain 1-Arrears. Every session, the MC gets hold equal to your Arrears that they may spend, 1 for 1, to either make a vulnerability pressing or have one of your contacts come to you with (as) a problem. You can buy off Arrears with an equal amount of Barter."