I'm giving LJ's new layout another try (it's ~80% of the way to convincing me to switch permanently) and took a look to see if there have been any changes to the new friends feed (~95% done, in my opinion.) And right at the top of the widget sidebar was a big "Login to Tumblr" button. Holy crap, they made my idea a reality. Now if only there were a way to repost from Tumblr to LJ like you can do with the Twitter and Instagram feeds and I'd be a truly happy camper.
If you want to check it out, first you need to be using LJ's new site design (click on the link on the homepage to test it out.) Then, you need to use the /feed page [
http://exampleusername.livejournal.com/feed/ ] instead of the /friends page [
http://exampleusername.livejournal.com/feed/ ], making sure to use your own username - the feed widgets are only visible to you on your own /feed page, not anywhere else nor to anyone else. And if you find the colors too bright/awful/distracting, click on the gear icon on the left of the page to choose your own colors for the /feed page.