Use friendfeed to view Twitter replies
Your Twitter replies can be viewed inside a friendfeed private (or not) group.

I now view my Twitter responses (@ replies and RTs) in my friendfeed private group, set up for that very reason.

First, we'll want to create our private group, by clicking on [Browse/edit groups].

In the groups page (which will be mostly empty if you don't use the groups feature), click on [Create a group].

Name the group and give it some basic settings. Here you can make this a private group, standard group, or a public group. Typically, for something like a private feed, you'll want to make this a private group, which is what I do here.
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Once you've created the group, you can set a feed icon so your replies can show up in your home feed on friendfeed and visually stand out. However, immediately I edit my settings to pull my Twitter reply feed.

Just click on [Import a service].

Choose the [Customer RSS/Atom] option. Twitter's search feed is Atom.

Simply type in @your_username to find replies directed toward you. Click on [Search] and await the results.

Click on the [Feed for this query] link. This will provide your feed URL, which we use in friendfeed.

Copy the URL in the address bar.

Paste it in the [Custom RSS/Atom URL] field. Choose your preferences, and click on [Import Custom RSS/Atom].

View the new [Active Services] and see your Atom feed from Twitter.

This display will be pretty plane jane, but very useful. The only thing you'll likely miss is a clear indicator of who replied to you and their icon. However, if you leave the link in play like I do, it will give you a simple quick link to Twitter's website. Obviously, one of my goals is to avoid dealing with their website, so I seldom click on that. You also can't easily reply in this space. You can, but the tool doesn't work exactly like the Twitter tools. I'd like to see a modicum of development go into improving this in friendfeed.
So far, there seems no simple method of importing DMs on friendfeed. But, this makes my social experience much simpler.
The icon is likely the thing I miss most about this interface. But, I see fewer blank icons or broken images. And, I spend less time on Twitter's website.