RF power measurement
Caveat: I have not tried this myself -- by the time you get this to work you will know more about it than I do.

Instead of putting your IF at DC, put it at some fixed frequency, say 1 MHz. Now you can run the signal through a a narrow bandpass filter to select out just the IF signal you want without worrying about DC drift issues. Connect the filtered signal to an rf detector (see also here and here). Now low-pass filter and amplify the detector output and use an ADC to measure the signal. This output will (within a certain range of input power) be proportional to the signal power you are trying to measure.  

Obviously there's more to it than that; if there wasn't Agilent, Anritsu, and R&amp;S wouldn't be able to charge 6 figures for a spectrum analyzer. But this ought to give you something to experiment with.

Edit 

After consulting this book I realize that a 1 MHz IF is probably not a good idea. It is preferable to use an IF outside the input band of the analyzer, to facilitate image rejection. For example, if you were mixing a 100 MHz signal down to 1 MHz using a 101 MHz LO, you'd also get any 102 MHz signals mixed down into your IF band. In the early-70's spectrum analyzer architecture discussed in the book they actually use 3 or 4 stages of up- and down-mixing to different IF's to achieve different filtering requirements. Their first stage mixes up above the input band to enable the best image rejection.