regarding the last two pedal points in Bach's fugue BWV 865

[rockingthebach]

So, it's literally impossible to hold the last two pedal points in Bach's fugue BWV 865 ( on the piano, at least, or also, I surmise, on the lautenwerk or the harpsichord).
If you use the sustain pedal, it blurs everything above it, plus, (as most of us are well aware) many find any use of the pedal in Bach verboten in general.
Henle ( whose fingerings I disagree with quite a bit, but I love their editions for visual clarity and general aesthetic appeal) seems to finger this final section as though you just play the pedal points as half or whole notes and then just keep going.
I am just curious if there is a standardized approach for this 'problem'. i hesitate to call it a problem, because that leaves me blaming Bach for something he clearly intended.
I have come to the conclusion Henle is correct; you need to play the note and just keep going, so the actual sustain of these pedal points is more in the audience/performer's mind or intention.
We can hypothesize all we want that the pedal point indicates Bach was clearly thinking of the pipe organ when he wrote this, but what are we poor, befuddled contemporary  pianists to do?
is  there some secret solution to this challenge that I am missing?
I googled this issue, but cannot find anything particularly relevant in several searches I have tried.
Thanks all, and have a good weekend.

[themeandvariation]

Use the Sostenuto pedal - the middle pedal.

[rockingthebach]

Thanks very much.
And after spending all morning reading up on the sostenuto pedal, it's nice to realize I am not alone finally saying to myself "So THAT'S what that pedal is for"...