I just installed the TinyPic Plugin to replace the removal of the Attachments option. This added the option to Upload to TinyPic when writing a post. It is at the bottom of the posting screen next to the Poll Creation and Options tabs.

You can choose either to insert a picture you have already uploaded, or you can choose to Upload a picture from your computer. Once it uploads, there is a button to Add to Post.
Please let me know if there are any glitches with this plugin.

Easy Peasy... No problems on my end.

Feel free to test it out in this thread - remember to use the spoiler though, especially if you don't have TinyPic set to reduce the image size automatically.