I tried out both Plume and Janetter, and both actually look really nice, and either would be a good replacement for TweakDeck, except for the lack of notifications. Janetter doesn't seem to have any at all as far as I can tell. And Plume either has notifications on or not, you can't choose specific things to get them for (like if you have multiple accounts, only alerting on new stuff in a specific account's timeline, or only when certain people tweet, search results, etc).
Plume really seems like the best match for TweakDeck at this point. It still needs a little work to catch up though. On the plus side, I see frequent releases on Google Play, and they have a nice suggestions board that they seem to be paying attention to, so it may get there eventually.
I've been using TweetCaster recently, which has an annoying splash screen, but otherwise is pretty functional (and very pretty). The one feature TweakDeck has that I haven't yet found in another twitter app is the ability to get notifications for new results of a search. It's hard to keep track of people mentioning your brand without that. So I still have TweakDeck installed just for the search notifications until it quits working, and maybe I'll find a client that does that by the time it does.
I haven't tried Janetter or Plume yet, I'll have to look at those.
And now I remember why I didn't like the default Home tab, even if I know which account it's set for. Because it's not a clean copy of that account's home timeline. If you tweet anything from any of your accounts, it shows up on that home tab, even if the account you tweeted from wasn't the default one, and your default account doesn't follow the one you tweeted from. To get a clean version of my home timeline for the default account, I still have to add it as a new column and just ignore the default one.
Also on the multiple-account issues, if you share a tweet via email, the subject line of the email always has your default account name in it, even if that's not the account you viewed the tweet from that you're sharing.
So I've discovered sometimes there is actually a conversation link right under the tweet when you view it. Sometimes there isn't, when it's something I know someone replied to (and I see the replies in a web browser). Does it only show up if the tweet in question is itself a reply, and not if there are only replies to it?
Feature request: Currently if you click on the context menu dropdown for a tweet and pick "Share" it shares a text blob containing the entire tweet in addition to the URL to the tweet. This works great if you're planning to email it for example, because you can pick your email client and you wind up with that as the body of the email. Every so often I find myself for some reason or another wanting to view it in my desktop web browser. Emailing it to myself just to be able to click the link is a pain, especially when Chrome and Firefox both have tab sync between the mobile and desktop clients. I'd much rather be able to share just the URL of the tweet, so that I can use the browser as a share target.
My main reason for doing this, however, is because I want to see a tweet in context (what "view conversation" gets you in the twitter web client). Implementing "View conversation" in Tweakdeck would remove my need for this. Implementing "Share URL" would probably be much easier though I'd imagine. :)
I'd like to echo the request to be able to remove the "Home" and "Me" columns. I have multiple twitter accounts (personal one, and a couple business-related ones) on my tweetdeck account, and multiple android devices, and each device seems to pick one at random to treat as the primary account for the Home page, so I can't get a consistant experience across devices. It also doesn't say which account it actually belongs to at the top, so I have to guess based on which items are showing in it. In order to get a column that has the account names at the top, I have to manually add the same Home column a second time, and just ignore the real one.