On the fifth day all was quiet for about 24 hours so took a gravity reading and it was at 1.030...hmm Stirred it up, added an ounce of Amarillo, and put it back in the closet.
Ouch. You shouldn't have stirred, unless you did so really carefully. Stirring after fermentation starts is a good way to oxidize your beer.
So my concern is: Was there enough enzymes in the specialty grains to fully convert all the sugar? Maybe it won't go any lower because nothing left but starch.
Possibly. You had a whole bunch of specialty grains, which are pretty much diastatically dead, plus some Vienna which had just enough enzymes to convert itself with a bit left over. Depending on the proportion of Vienna malt you could easily have had incomplete conversion. OTOH, you mashed for a fairly long time, so you might have gotten full conversion. Without knowing the proportion of crystal and aromatic malts to Vienna malt, you can't know for sure.
Good information on diastatic power here:
All that said, I wouldn't worry about it too much. I'm guessing that your mini-mash formed about 20-30% of the total grist. Since LME is usually highly fermentable and the Munich LME will ferment reasonably well, it will probably all balance out.
If not, next time add some diastatically powerful malt (e.g., Pils or American pale) to get full conversion and back down on the specialty malts. Also, no need to mash crystal malt; just add it to the mash before mash out.
I think that your current problem isn't related to mashing, though. I think you're just seeing incomplete fermentation, which should clear up with time. Assuming you're using an ale yeast, it's not unreasonable for a bigger beer to take a couple of weeks to finish fermenting. If you haven't hit your expected FG after a couple of weeks, then it's time to start worrying.
What would the beer taste like if it had a lot of starches left? Tastes a bit sweet but nothing too out of the ordinary.
Dextrin malts will make a beer seem really full-bodied and chewy - like a doppelbock or English barleywine - and your FG will be a bit higher than if you had a more attenuable wort. Excess starches in the beer might also give it a haze. Underattenuated beer will taste sweet, possibly even cloyingly so, but if it's just unfermented simple sugars in the wort, eventually the yeast will eat them and you'll get your expected FG.