I hope this may be helpful for others, and I hope others will also share their findings, so everyone may benefit.
After a good month with the latest forum version, I have found a way to carry on about as well as usual (however well that was).
I believe there will be further improvements in the form of customizations/corrections, so we get some of the lost functionalities and options back, such as the latest poster name and time since latest post, and hopefully the ability to go straight to the latest post, just to name a few.
The search is still rather weird, even weirder than before, and its now being hidden away in Overview makes it even less attractive to use. Hopefully there will be improvements there, too.
I also miss some options which are more unlikely to reappear, such as having the search on the Contents/Discussion page and 100 threads showing in the list there.
But as it is now, there are actually some things that are better than before the latest change:
The different background colours, making some posters more equal than others, have gone. Here are a few threads about those:
While you edit a post, it is now possible to see the post you are replying to, instead of having to rely on your memory of the details, sometimes having to go back and make corrections when it fails you.
As mentioned before, I am unsure whether it is owing to the change of browser version (to FF29, now FF30) which took place at about the same time, but the forums have been much faster for me (I was one of the lucky few without the sign in issues, even before they were (more or less) solved, independently but at the same time as the forum change);
The Translation option, even with its shortcomings (and its inability to look past something that might be the target language in the OP name or in the headline or in the beginning of the OP message, and I wish English would be first rather than last on the list), is usually sufficient to grasp the meaning well enough, much faster than pasting text into Google Translate which is now the last resort;
The new filters in the Contents/Discussions view can be quite helpful; Type to filter by text may be a quick alternative to a search if you remember the unique word(ing, not separate keywords) you are looking for, and the other filters may similarly come in handy to shorten the list of threads (Open/Answered/Discussion threads), and you can even start with the oldest ones (Sort by);
Initially just a nagger, the new number blob is still a nagger but it may be a very helpful one, an alert about new posts, so a look at any one forum in any one tab in any one window is (normally, see below about social media speak) enough to know at a glance whether anything new is going on anywhere in all the current threads you are involved in; this may be tied to a (lucky) workflow where you have a quick look at the forums a number of times a day, and where the threads remain relevant as long as new posts are added (I have only needed to stop following a Spam thread and maybe two others, at most); with the number blob you can quickly find and follow up, and decide whether to have a further look round for new threads or just leave until the next quick look.
The social media speak about acclaims, changed connexions, and whichever other unintelligibilities, add to the number in the blob, but you can see them and rid yourself of them by clicking Mark all read in the Inbox (see below about that).
All in all, I have kept on as usual or adapted in the following way, for highest possible efficiency:
Business as usual:
I still have the relevant forums bookmarked with the Contents/Discussions/Detail view;
I still have perpetual browser sessions with all the relevant forums opened in different tabs in different windows, opening at startup every day;
In each forum I still open all the threads (with new posts) I am going to look at in separate tabs in one go, the last one replacing the thread list, and then go through them and close them one by one, apart from the last one where I use the bookmark to reload the (now updated) forum thread list, sometimes in repeated rounds when there are busy threads;
I still have a quick look at the forums a number of times a day.
I use the number blob as an alert;
I have my Inbox open in a separate tab so I can click Mark all read at any time, to rid it of unneeded items such as social media speak, and so I can see at a glance what is going on where;
I use the Translation;
I use the filters now and again to find threads more easily.