Use Reign to model competing spy networks. Use Ars Magica to play Spy v. Spy with your PCs being spymasters
To amplify Gomad's point, Both Reign and Ars Magica have excellent spy-network subsystems which I've used.
The Reign company rules do not require sovereign rule over a territory, as multiple companies can spatially co-exist. Therefore, they are perfect for modelling competing spy networks and providing a largely abstracted but manipulatable way of gaining information, sowing disinformation, and tying the actions of the PCs into the consequences of spy success or failure.
The Ars Magica agent rules (found in Houses of Hermes: Societies are far more specific and crunchy, though easily adaptable to any given system. They provide for hierarchies of agents, their advancement, and all standard espionage actions. They are far better than Reign's rules for spending quite a lot of time exploring the spy game, but thereby take more time and effort to resolve.
Amusingly, the systems can even be combined without too much effort, although the complete combination would be the answer to another question. (hint, hint.)
Erik's answer is a great general solution to your problem, but there are a couple of specific tactics you can use here as well.
Put Your Eggs in More Baskets
Right now, you're relying on a single skill or small group of skills in order to give your players information about the game world. This is naturally going to lead to situations where nobody has the skill you need, plus it makes story progression hinge on the outcome of a roll, which is very risky.
Instead of making everything a capital-K Knowledge roll, allow your PCs to use the skills they do have as knowledge skills. A fighter should be able to roll Athletics in order to assess someone's physical fitness. A rogue with Sleight of Hand might be familiar with a number of local pickpockets. This emphasizes each character's specialties, and encourages them to gather information creatively using a variety of methods. Skill descriptions are often left open-ended for precisely this reason.
Give Away Information
Like I said before, having the progression of your story hinge on a die roll is risky business. What happens if the die roll fails? Does the plot just stall? If the answer is yes, there probably shouldn't be a die roll. Instead, find a way to justify giving the information to the players based on their competencies and backstories. So, in your example:
The door opens with a slam , and a tall figure in full plate strides
into the tavern. Joe, because you spent time on the city watch, I can
tell you that this is a watch commander. Greg, you're trained in
survival, so you can tell when someone is looking for you, and this
guy definitely is.
Giving players "automatic successes" like this not only helps move the story quickly past less dramatic moments, it also rewards characters for having a backstory, and makes them feel more competent and embedded in the world.
Overall
Look at non-knowledge skills as representing non-book-learning types of knowledge, and use those skills as hooks for dishing out free adventure hooks.
Best Answer
I haven't found a generator there that exactly matches your needs, but you should look at Abulafia.
Being a wiki, you could even make a new page for a Side Quest Generatator that generates imperative phrases as in your example, using the site's existing item lists to fill the blanks.