Jetpack doesn't connect to wordpress.com

This is on https://lmashton.com

I started having problems with Jetpack about a week ago when I tried changing the facebook sharing setting. I then disconnected my wordpress.com account today and tried to reconnect it several times. It failed, giving me the 32700 error message saying something like something just went wrong that wasn’t supposed to.

I then deactivated jetpack and deleted it, then tried installing it again through the plugin install manager. That failed. I logged in through ftp and removed the existing jetpack folder in the plugins folder, then uploaded a newly-downloaded and unzipped jetpack, latest version of course. And I activated that. I got the following error message:

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Your Jetpack has a glitch. Something went wrong that’s never supposed to happen. Guess you’re just lucky: xml_rpc-32700
Try connecting again.

Error Details: The Jetpack server could not communicate with your site’s XML-RPC URL. Please check to make sure https://lmashton.com/xmlrpc.php is working properly. It should show ‘XML?RPC server accepts POST requests only.’ on a line by itself when viewed in a browser and should not have any blank links or extra output anywhere.
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I then deactivated all plugins and reactivated jetpack and tried connecting again. Same error message. I then changed the theme to twenty twelve and tried again. Same error message.

So I’m sitting with only jetpack installed, no other plugins, and using 2012, and I still cannot connect to wordpress.com.

When I type https://lmashton.com/xmlrpc.php into the browser, it comes back with the correct message, indicating xmlrpc theoretically works. When I go through the debugger at https://jetpack.me/support/debug/, it tells me “XML-RPC is not responding correctly ( 200 )”. When I run MarsEdit (a Mac app for blogging), it has no problem connecting, which seems to indicate that standard xmlrpc is working, but perhaps jetpack does something different? By the way, I ran MarsEdit for the first time *after* I did everything else I listed above.

What now? Do I delete everything, install wordpress from scratch, and upload my database? Or is there something else I can do that will fix this?