Sure:
1. Analog Devices has a good series. ADXL202 is a good device, +/- 2g.
2. DIPs are obsolete. Frankly, industry does not want them and no modern devices are likely to be available. LCC is common. So get an eval board with the proper pads, etch your own, or send it out for mfg. It's not that expensive these days.
3. I don't think there's any way to get 0.001G accuracy. They're inherently noisy devices! Plus the offset error and its drift are far, far larger than this. You could do massive oversampling or filtering to try and ditch the noise, but it can really slow down your system and will do nothing for the offset errors.