I toyed with the idea of making an online version of netrunner for a while recently, potentially just for private use (both jinteki and octgn don't really do it for me, though of course jinteki is really getting there). However I came to pretty much the same conclusion mentioned in the OP that it has a problematic structure, and so took another look at how jinteki tackles it to see if the UI could be improved upon.
I ended up doing blackat instead, supposedly as a warm-up for it really, but honestly I doubt I'll go any further with the client idea for various reasons. One of them was just simply that, yeah, it's not only a hard game to move onto digital with serious elegance, but also those same issues are indeed present in meatspace too (see above with the constant False Lead check) - while normally they're not an issue this only really happens by assuming certain things for the most part, not having to actually observe the paid abilities windows properly all the time and being allowed to reverse your plays if you're too fast. The truth is we're very unlikely to fix it in digital while these issues still exist in analogue.
So, then comes along this idea of a tweaked, streamlined version of ANR, which is something that I've pondered too, but not directly - I was thinking more of filter out the cards from my collection that create rules issues and seeing what I had left and what play experience that might give. Not sure, will have to see on that one. Really this is just a thought exercise on my part because I like to think about game rules and mechanics. It's interesting to notice that other people are thinking along similar line
Ultimately though, as mentioned, nobody wants to play 'almost netrunner' (or at least very few). Making an online client is a whole heap of work, and making that for a niche segment of an already niche audience would take some serious determination with potentially little external reward. It could well be a significantly better version that may even have implications for analogue play if you really fixed the timing, but then it's just not the official thing, so you're still screwed.
Probably the most effective thing to do is to take the rules, improve and streamline them, then - sadly - re-theme it so you can package it as a different product and actually gain traction like that. But then you're talking artwork etc.and it's no longer netrunner, so what's the point?