Given your stated requirements, I'd use Qt. There's a learning curve, but no worse than with WPF or anything else.
But those are hefty requirements for a small in-house project! Spending a lot of extra programming time on production values is what you do when you're trying to appeal to the mass market. If nobody outside your team is ever going to use the program, that kind of effort doesn't pay off. Who decided the feature list and designed the user interface? Do they realize the cost and schedule implications?
Maybe I oversold the feature list... I'm really just trying to do an incremental thing, a "single-page app" that helps tech support agents keep track of their tickets and what's going on with the rest of the team. Because the ticketing system is web based I figure I need to embed the web pages into the app. Then I need to make DOM calls to the page to get some info out of them, or perhaps make various GETs and POSTs to get the info I need, displayed alongside the webpage.
Not a crazy feature list, and like I said I am learning how to do this from scratch so it's kind of a 20% time hobby that I hope turns into something usable in a reasonable amount of time (3-6 months).
But those are hefty requirements for a small in-house project! Spending a lot of extra programming time on production values is what you do when you're trying to appeal to the mass market. If nobody outside your team is ever going to use the program, that kind of effort doesn't pay off. Who decided the feature list and designed the user interface? Do they realize the cost and schedule implications?