"I guess the question is, if I applied the Maple stain first and don't like how it turns out, could I put a second coat of Iron Nitrate over the LMF stain and rub it out again? Or is the right order of process, Iron Nitrate first then stain last?"
Iron Nitrate first then stain - yes, that is the usual process with Aqua Fortis (Iron Nitrate).
I think you had it with that first try, as shown in your first photograph. I also believe that your particular wood is more rich in iron unlike that example you show in the second picture. Every piece of maple reacts somewhat differently to AQ than the next one. Either that or the the application of the tannin caused the overall darkness. Tannin is supposed to accentuate the figure, after you put that on is the time to rub it back some. So, when you put the AQ on she really went dark, but even so that might have looked good once your finish went on because the finish lightens the wood a few shades. Did you try rubbing on some mineral spirits, or even water, as a visual check of what the finish coat would look like on your "too dark stock"? I would bet that reddish toasty brown would have popped right out at you.
Before I commit to a stain over AQ I do some testing in the barrel channel, that will give you an idea of what your AQ and stains will do.
What to do now; If it were mine I would do another AQ treatment and afterwards do a check with an application of mineral spirit, just wet the stock somewhere and see what your final finish will likely bring out. If you think the stock will benefit from that LMF Maple stain test it in the barrel channel to see if you like it.
dave