Hmm, I've not dealt with this particular problem before, but I have dealt with problems involved in successfully converging huge (100+ 24MP) panoramas.
In either geometric or photometric alignment, the local parameters (img position & exposure/color) must be "close" before turning on the global (lens model) parameters or exactly the local extrema you point out will prevent selection of the right answer. Because the lens params affect every image at once, their influence over any means of solving the optimization (gradient descent, annealing, newton-raphson, levenberg-marquadt, ...) quickly becomes very dominant & will cause the optimizer to walk down wrong valleys.
I'm sure we've all said "sure, align brightness, color balance, vignetting and camera response at once" and seen things like the hue drift off at a fixed rate departing from the anchor image, for example.
First the geometry has to be as close as possible to right. I usually first align one group of up to about 20 images with only angular parameters (no translate, no lens).
At this point I'd do camera translate.
Using only these, I then let it do HFOV. Then distortion params 1 by 1, c then b then a.
Then fix lens, unselect the first 20, and add a new 20 at their perimeter, continue until all are aligned.
Now a global align is needed... If there are a LOT of images (>= 100), leaving lens params on is usually a bad idea I find.
For "good" panoramas (tripod and no near foreground objects), this generally for me achieves an rms error of perhaps 2-4px.
Photometric alignment is a PITA with many images... It has the instability problems like geometry & distortion params, but MUCH worse for lots of pics. But for mosaicing I imagine that trying to force the color rms error under 2/255 isn't such a priority, but I recommend the same basic strategy: photoalign a group of ~20 pics, brightness first then WB then vignetting & cam resp.
I don't think I've ever gotten a satisfactory large global photometric that included lens in the global optimize...
I hope some part of this rambling proves useful!