Wide zooms.
Analyze your use of the 10-20 and see how much of the time you use wider than 12mm. The other thing to check out is to see how accurate the 10mm and 12mm are in real life. I am sure that the testing facilities can come up with numbers. Many lenses overstate the numbers a bit here and there, and you might not be as short as you think.
That will tell you whether or not the 12-24 will cramp your style. I am very happy with the field of view of the 12-24, and its optical quality is even better than I had hoped when I bought it. The distortion is low enough that I have even done panoramas stitching it together over 360 degrees, just to see what would happen. Another lens to consider would be the 10-17 fisheye for when you need wider than 12mm. The field of view is even wider than the Sigma at 10mm because of the type of lens it is. I personally dislike the fisheye look most of the time, but the odd fisheye image does strike me.
Normal zoom?
Would you be happy with a normal zoom such as the DA* 16-50 or DA 17-70? I am one of the happy campers with the 16-50, but there is a lot of overlap with the 12-24. The 17-70 might be a nicer fit while still keeping SDM. This could replace a lot of the primes with a single lens with more than adequate quality.
Short tele zoom
I have the DA* 50-135, and frankly, it is a marvellous piece of glass. In film days I used the A 70-210 (and still have it!) and that was a perfect field of view range. In digital, 50-135 is almost exactly the same range. It fits me. It's weather resistant so I can use it outdoors without panic, and focuses very quietly using SDM. In view of the SDM reluctance on occasion, I will be checking the lens out very carefully this fall, just before the Canadian two year warranty runs out and shipping it off to be repaired at Pentax expense.
Moderate tele zoom
I use the A 70-210 for this range of coverage. Interestingly enough, I seldom use anything between 135 and 400, so it is seldom used. That, of course, is just my usage, and in case of necessity I can put the 1.4X-S on the back of the 70-210 to get 100-300, filling the gap nicely.
My kit
I carry, most of the time, four lenses only. they are the DA 12-24, DA* 16-50, DA* 50-135 and my elderly but good M 100 macro. This covers everything but wildlife photos. You have the Sigma 105, so that's a keeper from all I have read. I would seriously consider the DA 17-70 as a replacement for the 16-50 in this lineup, depending on whether or not you need/want f/2.8 all the way from 16 to 135mm.
That's my shot at your question. As you can see, I am not a much of a fan of zooms that go over 3:1 focal length ratio, despite the convenience. That said, there are quite a few 3:1 or less zooms that are more than adequate quality. All three of the zooms in the list are covered by DxO Standard correction software, so they are almost "perfect in every way."
You can also see, that I am not a fan of lenses by other companies. I have tried them on occasion, and always come back to "the Pentax look." I had a Sigma 75-250 with matched macro "filter" for a while, but it was mechanically not up to snuff, although adequate (barely) optically. The latest escapade was 2003, when I tried the Sigma 170-500 as a possible replacement for the 400. It was much softer than the 400. I've pretty well decided that Asahi Optical will make (or oversee the making of) my lenses. I am sure that I am rejecting out of hand a whole bunch of superb lenses this way, but my kit right now is about as close to perfect for my needs as I can get - once I add the K20 to the mix, of course, and the 55-300 would be handy ...