If I were to look for a job now with a portfolio of the products I've worked on at the company over the last year, it would definitely be an uphill battle.
I'd recommend doing as many side projects as you can. I know it can be hard to find the time (I have a one year old son so I'm familiar with the struggle) but if you can put something together over a few nights/weekends, and really design the hell out of it, it'll make stomaching your day-job constraints much easier. Just remember the Sex and Cash theory: http://gapingvoid.com/?s=sex+and+cash+theory What you do at work is strictly to pay the bills. If you happen to enjoy it sometimes, great; but remember that what really matters is what happens outside of that.
Another example: I used to flip burgers, but I enjoy cooking at home. I wasn't ashamed of the nasty food I pumped out of that fast-food kitchen, because I knew it wasn't a representation of my cooking abilities, it was just what I did to pay the bills. Apply the same thinking to your situation.
I've found absolutely fantastic designers who are struggling through go-nowhere jobs in the depths of enterprise companies that don't care about design, design agencies that are structured like puppy mills, and the like. When finally given the opportunity to build their vision, they excel.
The designers who have "designed apps you admire" are just the obvious, low-hanging fruit.