Wanted: TT clip-on bars 31.8 mm

TT clip-on bars that look like this ____/ (well, with a little bit less incline, unlike J-bend), are adjustable in length, have arm pads adjustable in fore-and-aft and last but not the least - have arm pads that sit a little bit elevated as compared to the handlebars base height?

I think Profile Design T4+ (along with a spacer kit) tick most of these boxes?

Thanks.

You may be best off getting the pad/clip section and then adding the extensions to suit. Most are 22.2 mm except Deda which are larger.
I went through many bends before finding any I like and also you may find your needs/ style/ flexability evolves.
USE are great because they do various degree bends and they can be inserted either way round (that's how some of the guys get the bars quite high infront of their faces (and still be UCI legal)).
I have had the Deda (in various formats) on my road bars and actually ended up buying 2 sets of clips so I can adjust the extensions independant of the pads.
I also found that the higher the area you hold the less stable the ride so more suited to higher cadence - I prefer lower extensions and whilst I like high cadence the set up feels more positive which is more important on road than track where I had the extensions higher.

OK, thanks but I think that only Profile Design have arm pads that are adjustable fore-and-aft (in a considerable extent), because they are mounted directly on the actual extensions, rather than the clip sections, correct?

Yes I think Profile have made several that do that but T4 probably the best bet. I think you can then swap out the extensions to most other makes to find the perfect bend. I found that some set ups that seemed perfect soon developed areas of discomfort (not that a tt set up will ever be comfortable).
I used 2 seperate set ups together (one for extensions and one for arm rests because I wanted to tilt the armrests). But not the prettiest of arrangements.