Wow, thanks for all the responses. Although I had been hoping for a strong consensus to "do 'xyz' " so that I would not have to do any thinking/make any decisions on my own, it is very valuable to have the different perspectives about it.
I didn't know I could transfer in-kind to my taxable account, it had been set up to automatically pull the appropriate RMD amount each year, and it looked like the Fidelity auto-process changed a portion of the shares to cash and put the cash into my taxable core position, so I thought that was the way it had to be done.
I had assumed I would be spending the money (because I'm retired and I thought it would have to be withdrawn as cash, and since it would be taxed as income it seemed logical to use it as income), but the 'in-kind' option would make it less risky to leave a bunch in equities because I could avoid selling in a down market by doing the withdrawal in-kind and instead use cash/bonds from the taxable for that year(s) spending money.
Never occurred to me to use the inherited IRA to house bonds to adjust overall portfolio AA, but now that you guys have put that in my head I'm thinking that might be a good plan. I'm not sure how far off my target AA I am but since equities keep going up this year, it is probably time to shift a bit more into bonds.
So now it looks like my plan will be to modify the AA in the inherited IRA to be somewhat more conservative, then I'll empty the account over the four years with proportional selling of equities and bonds (and spend the money as income). But if the market is down I'll move equities in-kind to the taxable account while using some of the bonds to cover the taxes. Yay, I got a plan, thank you all!!