Maybe rather the Omnifactory gambling, or making it a convoy, you can just reduce how much the Omnifactory pays to sell things to it? 1/4 sell price but learn to produce them or full sell price at another station. That would stop it being the one stop sales point it currently is, and make you think about what you want to sell where. If you are changing sales prices, i would also recommend making hostile stations pay half. Give you a reason to not sit on top of the pirates and farm them to sell them back gear to make fleets to farm. (I know this isn't how it works, but it is how I like to think of it)
My main problem with making it a random chance to produce is the chance of a scenario like this:
Fight my 5th Uomoz's fleet, and finally get an unsung.
I have enough fleet points that I could use two of them, so lets take it to the omni factory.
It analyzes it, but fails the check to make more.
I miss this message because, like many messages, it chooses to pop up right as I enter a station or a battle, and I have no method to see the message log.
I keep checking the Omnifactory for my prized Unsung to show up, getting increasingly frustrated with it.
Yay, random..
Being able to hire specific convoys would be nice, but to my understanding you can't implement any sort of new inv/dialog to hire specific, so it would have to be a new station, or a complete rework of the current station. Probably a new station because if you are hiring a fleet it would likely need to be a token you buy somewhere else and put someplace. The other problem I see is that unlike this current set up where you trade immediate access for production long term, hiring a convoy would what? Take away your current item and bring two? take away your current item and bring it back at a loss of time and money and potentially loosing the convoy? Add the item to a random pool of what the convoy brings, and do like the race stations seem to do and NEVER bring anything above a cruiser ESPECIALLY if you have the audacity to want to try fighters or frigates? Adding the item to a random pool of what a irregular convoy brings seems like it would be less about hindering people who know what they want delivered (only sell 4-5 items to the convoy spawn station) and more about frustrating and hurting the gameplay of people who like diversified fleets, or new players that have no clue about what exactly they want delivered.
Uomoz, I think of the omnifactory less as replacing current mechanics, and more as a stop gap measure for mechanics that aren't in the game yet. It is, of course, your mod so feel free to change it as you desire. This is just how I think about it.
tldr:
I think lowering the price the omnifactory pays you is a good idea, the other solutions seem overly minmax-y (regular convoys), detrimental to play ( convoys for new players, gambling for anything unique or hard to get)