Although my group, too, was disappointed by the new CB's lack of house-rule support, we quickly discovered that as long as we took the feats that made a mechanical difference to the character sheet, we could just type the other ones in another place (campaign notes, for example). We know what feats we have and where to find them, so whether or not they show up in the box labeled "Feats" is a non-issue. And really, only a few feats have any mathematical impact on the sheet; just make sure to include the ones that do in your "real" feats and write the other ones down.
On a related note, my group also uses inherent bonuses. We discovered that the new builder can handle inherent bonuses, there's just no way to "turn them on." We got around this by using the old builder to create an empty character with the inherent bonuses box checked (i.e. a saved blank character file with inherent bonuses turned on). When you build a new character in the web-based CB, just import this file and build from there. The inherent bonuses will work fine.
While neither of these "fixes" are ideal, they're both really simple and eliminate most of our complaints about the new builder.
The other complaint (no export) we get around by printing our character sheets as low-rez pdfs, then e-mailing them to our DM. I expect that will be the first new feature added to the CB, but even this, now, isn't a priority for us since the workaround is so easy.
I know a lot of people will say, "I shouldn't have to do all that to use the new builder the way I want," and I think it's fair to feel that way. On the other hand, I am willing to jump through a couple of hoops in order to give the new builder the functionality I want it to have, and doing so has taken me from unhappy with the CB to happy in very short order.