This is why I take the darks during tear down. The camera can sit there and take noise pictures until I'm finished tearing down by big heavy wooden tripod, packing up the big lens, and loading all of the crap back in the car. It takes a good 15 to 20 minutes. Which gives a good set to create a master dark frame for the session to drive down the random noise so that one can get a good picture of the actual nose from that portion of the camera system.

Actually by averaging noise images you are actually driving down the truly random noise portion and this obeys the 1/sqrt(# shots) rule. The only way to get rid of that is as you say to collect more light frames. Getting rid of the random noise in other shots like darks and bias frames is also desirable so that you can clearly see the systematic noise, or probably more correctly call errors, from various components. The lower the errors of these components the more shots you need to move the true noise floor below these. Now I actually don't know where these levels are but it might be a fun experiment to undertake some time and I kind of want to. It is suppose to get cloudy and crappy tonight so I might waste some time doing that because I can. I will probably use an existing set of bias frames (I think I have a really big stack at ISO 100 that might be over 400) and see at what level one can see start to see the systematic error from various average stacks. I will go and shoot a big pile of darks while I play with that and do the same. The method of processing will be to develop in Rawtherapee to 32 bit tiffs, load a stack into GIMP and average them and flatten into an image. Then up the contrast and play with levels to see if it is showing noise or systematic errors.

To be very clear (because I'm not sure it will be to anyone else reading this) averaging dark frames only reduces the amount of random shot noise that is introduced by using dark frames in the first place. It does NOT reduce the random shot noise caused by the dark signal that is in the light frames. Only more total exposure can do that. (Note that the non-random component of the dark signal is actually mainly suppressed in all but the very oldest cameras, to varying degrees of success.) Use of a master dark frame WILL add some random shot noise. But if you averaged a lot of dark frames to make your master dark, it will be small. Similarly, using a master bias frame will not reduce the random component of read noise that is in each of the light frames. In fact, it will introduce more (but again very small if you averaged a lot of bias frames). A master bias will only reduce the non-random component of the read-noise signal.

Hence, using dark frames and bias frames DOES add extra noise to the image, the amount depending on how many frames were averaged for each. But this hopefully small amount of extra noise is better than leaving FPN, which may include amp glow, in the image, which is what dark frames and bias frames (if there is a non-random component to the read noise) are designed to eliminate. Dark frames also get rid of hot pixels. But there are several alternative methods of getting rid of hot pixels including dithering. (Dithering can also reduce the magnitude of FPN to the point of insignificance if it is not too severe.) Those alternative methods do not add any extra random noise.

All of that said, if the sub-exposures are exposed properly the read noise will be insignificant compared to the overall signal (sky background + objects). And in the presence of even a moderate amount of light pollution, the random noise introduced by the sky background will swamp even the random thermal noise from most of today's cameras on all but the warmest nights. So, random read noise and for many people also random thermal noise are the least of the random noises one needs to worry about.

(Some may object to my putting "random" in front of noise. But I do that because some people also define non-random components of a signal as noise if those non-random components are unwanted. I find that usage makes discussion harder. However, given that usage I want to always make it clear when I am talking about random (shot) noise.)

That is why I divide things into the true random noise and the systematic noise or probably a better term for it systematic errors. If trying to remove the systematic error then you need to drive the true random noise down below the level of those systematic errors. In my poking around so far it looks like with my K-3 I might just barely be seeing some of the error to be captured by the bias frames when I stack 16 of them but it is slight. Even going up to 36 shots in the stack it still isn't really bad but in a few of areas it is clear there is some systematic error but there is still a fair amount of noise at this level. The fact the I can pull it up some systematic error at a 36 shot level with bias frames (ISO 3200, 1/8000s were the settings used) would seem to indicate that the read noise starts around 4 bits below the shot noise and starts becoming noticeable around 5 bits below it. So to push the noise down further from there to get a good picture of it you would probably want to push the shot noise down another 2 bits which would mean you would need at least 128 shots total but 256 shots would be better getting the noise floor from the shot noise down to 4 bits below the read noise. I took over 500 bias frames at ISO 3200 but will probably do one more stack tomorrow that is a stack of stacks since I don't want to do 100 at once so instead I will stack 4 sets of 36 since I have one stack of 36 already. That will give a nice stack of 144 which would push the shot noise down a little more than 7 bits.

So the takeaway here is if you have a K-3 or K-3ii and want to use bias frames you really should be taking at least 100 bias frames but 200+ is better instead of the 20-30 that was recommended earlier. At 20 -30 shot noise is still playing a big part there but you will start to remove the read noise.

Since I'm in an area that is really light polluted and ISO 1600 is about all I really want to use even with a light pollution filter that just can't filter all of it out I may just give up on using bias frames. However for those times when I can make it to a darker area (looks like tomorrow night might be a good one and hopefully next weekend will play nice too) I would probably still consider using them.