Both are perfectly valid and both are, as you have discovered, present chalenges on the fretless bass. I thought about looking at each in turn, but actually they both boil down to the same thing: having a hand that is not 'locked in'. For a lot of people they get caught up in the idea that you have to keep all fingers in position all of the time, even those that are not playing notes. This is true of both 3-finger and 4-finger players. The books will all tell you to keep your fingers over the adjacent frets at all times, and some even go so far as to say keep the lower fingers down on the strings behind the stop. This is not necessary. I've said it before but it is worth re-iterating - check out the left hands of some top-class cellists (Yo-Yo Ma, Jacqueline DuPre or Sheku Kanneh-Mason) and see how fluent and free the left hands are, how they glide between tip and pad, how they use the thumb to establish position and how the fingers lead each other around the fingerboard.
IME the Barre is is just a question of alignment. The most tricky part is freeing your hand to facilitate alignment of the finger for perfect intonation at both contact points. Dont be afraid to lift the other fingers away from the locked-in position. You can still do this and maintain good handshape.
In this first picture, Barre with Index, it looks like by middle finger is pressing down on top of index but it isn't - there is no contact:
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Likewise, in this next picture it looks like Index and Middle are supporting the stop from behind but they are not - all other fingers are lifted:
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Again, in this final picture, only Pinky is touching the strings - the others are lifted:
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With separate fingers it is still about alignment, and for that you need to create space to accomodate both stops. So try to play with as much of the fingertip as possible - this creates the space you need to to get both fingertips down side by side. As before, Index and Middle are off the strings:
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And once more, playing the 4th with Middle and Ring - Index and Pinky are not doing anything, but they are 'ready' to drop into position for the next note, whereever that might be. In this particular image the index was playing the low octave, but has lifted to enable the hand to realign for the double-stop:
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