In the opening most of the pedalling is designed to presrve the C# in the bass, but not all of it. Why the hiatus?
Hmmm, interesting question...my guess is, either Chopin didn't intend to preserve the C# in the bass, or he didn't want the harmonic progression muddled up and thus wrote no pedal marking (end of bar 1 and start of bar 2). Or neither. Anyway, usually I believe most people will use half-pedals to preserve that bass note to some extent, without blurring the harmony. Some preserve it for the entire line, and some letting it die progressively halfway through. Your choice.
Then once the barcarolle bass begins in bar 4, the pedalling runs across the phrase markings, which it seems to me makes no sense. Or am I thinking too classically- would that attention to phrasing not make sense in romantic music?
Surely the Barcarolle begins in bar 1?

But the boat started swelling to the little waves in bar 4 for sure. Just to confirm: in bars 4 and 5, Chopin marked pedal changes in both A# in your score yes? (and of course at the beginning of each bar) And I think it is to reflect these swells that Chopin had that pedalling in mind. You can run the semiquaver notes (or 16ths) a little towards that A# without articulating too much to reflect that gentle sway.
But when the melody comes in bar 6, for sure you want to avoid blurring the sound by overpedalling, so yes you need to change the pedal a little more often. Essentially, remember that although Chopin wrote so much pedalling, it's imperfect. He couldn't tell you to flutter pedal or half pedal for instance. So you need to use your brain, ear, and musical intuition wisely to determine the pedalling in such places.
The tenuto markings I love in the second section (pocco piu mosso bars 42, 46) and I maintain that feeling in octave versions of the same tumbling phrase( bars 53, 57). I also bring it back when the figure returns in 103, 104, 107 and 108, but perhaps now I'm being to schmaltzy and romantic? These sorts of things, and the very different dynamic choices of the performances I've listened to on the internet, make me wonder how much of the score I can assume is Chopin's.
Well, the others are not marked "tenuto", so what is your reason for doing so for similar figures in the rest of the piece? You know, there's more going on than just that G# note landing after the harmonic change - namely, the echo starts there too at first, and then when it came an octave higher and after the climactic piu mosso, the echo starts a note earlier than where you'd put the tenuto in.
Anyway, what you're doing is not necessarily wrong, but it is wrong if it is not for the right reason!
As for other people's performances, well, don't worry about them too much. You know people understand and perform Chopin's music differently according to how they read and understand the score. And as regards the score, well you know, teachers and artists have their own preferences too! Some consider Paderewski the most musically satisfying, while some consider it academically flawed. And some consider the Henle simply arrogant. So...actually the problem stems from the fact Chopin signed off those 2 first editions that have quite a few subtle differences - which are then different again to his original manuscript!
I am learning it by myself. Although I certainly need a teacher I haven't been able to find one in Blantyre, the nearest city of any size.
...I'd try to find a good teacher if I were you, even if to play it just once when you feel you're ready. It's just such a gorgeous piece it's a shame if you don't get to learn it really well.