Dear Zen - I'm sorry I was harsh. It was uncalled for, and I apologize. You're right - as soon as I started, I should have realized that I was being inappropriate.
Let's start again. Your job is being replaced. THat sucks. However, it's not realistic nowadays to expect companies to keep a job open if they can find a cheaper way of doing it. However, they must like your work if they say they're trying to find another position for you. What I was trying to say, though (however badly I managed it) was that you have to impress upon them that you'll be eager to learn a new position, and do it well. By saying you liked the "boring and mindless" aspect of your old position, you sound like you're not up to it (and yes, in the morning light I realize you're probably being deliberately ironic in youe phrasing, but if you repeat it to management, they may jump to the same conclusion I did).
My recommendation is to think of your situation now as if you've been working on a contract. The contract is over, so you want to "sell" the customer on using you for something else. This calls for some evaluation of what YOU want to do, and showing the employer WHY they should put you in a new position. Is there a position in the company you think you'd enjoy? If so, tell them what it is, and give them reasons why you can do it, and make a success of it.
Of course, you should also be looking for "new" clients - even if the management thinks you're worth keeping (and they clearly do), they might not make it fit right now. So, I recommend trying both approaches; sell yourself and your skills to your own company, but start checking out new employers as well. In the competitive world we face today, you've got to let them know why you'd be a good choice.
I'm afraid the bitter tone I took last night can be blamed on fatigue, but also you have sort of a "laid-back" sound to your post, which isn't what you need right now. You need to make them think "Zen is a firebrand, and would really make this position her own", not "well, Zen's worked with us for some time, and wasn't wretchedly bad, so I suppose we owe her a new job". Unfortunately, even if that's true, it's not how companies think these days.