You could set up a dedicated server and configure all the necessary software you'd need for this, but unfortunately it's tough for us to say how much power you might need with the dedicated server. And you'd have to set up the software yourself, as the software side of it is outside our scope of support (We do set up your dedicated server and take care of the hardware for you though).
Ultimately, if it's not a big event making a lot of money, you probably will not want to spend the time and money on that dedicated setup. You should continue trying with similar services to the ones you mentioned for the most part, but we can try and help with the dedi if you do want to give it a try!
We did recently have a customer of ours running two live streams on their site, which they rigged from home using a local PC as the streaming server. You can see a basic explanation of what they were using, here:
If this is for something temporary, you could try following their example with a home PC and see if that works!