Is there any further significance to the choice of Verdun as battlefield?

I think that everything you said makes complete sense, but I see also that there was a previous "Battle of Verdun" during the Franco-Prussian War:
http://en.wikipedia.org/wiki/Battle_of_Verdun_(1792)

The 1792 battle occurred over a single day, and the Prussian army successfully defeated the French.

The 1916 battle, that you mention, occurred over 11 months and ultimately the French army defeated the German army, despite an initial assumption (by the Germans) to the contrary.

Looking at the plot of the movie, the Mimics' plan is revealed to be that they are staging battles and when suffering a loss, they repeat the day, remember the previous events, and then go on to seem prescient and win the "second" version of the attack.

Everything was working perfectly with that methodology until Rita steals the time-reversal power, and now she remembers the battles and they do not, because she is the one resetting the time-line. She eventually loses this power, but Cage garners it in a very similar manner, and this is the focus of the movie. We only learn about Rita's experiences through dialogue, and she is situated as a mentor to Cage.

So, if we ignore Rita's experience and simply look at the movie and the references to Verdun in regards of Cage's experiences, I think that the history of the two battles mirrors the plot of the film.

The "first" time through, it was an unequivocal defeat for humanity. But now that Cage has the power for time-reversal, despite the loooooong and arduous task of training and dying and training and dying, he ultimately defeats the mimics and wins the war.

I think the specificity of the choice of the battle site is because it has this very unique history of being a site of an extremely short and then an extremely long battle. The mimic attack that Cage first went through was clearly going to be a quick defeat of the last human defense effort, but by being able to restart the time-line, he was able to then endure this incredibly long battle and ultimately succeed.

Some historians believe that the German attack at Verdun was a ruse aimed to lure the French into responding in an attempt to retake the city. The Germans assumed the French counter-attack would be in vain in the face of their overwhelming artillery fire and that they could destroy the French army on open ground in a confined space. The idea was to destroy the French ability and will to fight further by making it too costly in manpower. So the parallel might be that the Mimics in Edge of Tomorrow were luring the allied Earth Defense forces into a counter-attack where they could be not possibly succeed, allowing their attacking armies to be destroyed en mass.

Based on the map seen in the beginning news real, and behind General Brigham during Cages railroading, all of Western Europe is infected with Mimics. France, Germany, all the way across to Romania and Western Russia.

Operation Downfall is staged to push in from the French coastline (British Channel, Biscay and Mediterranean, Spain), Lower Italy, Scandinavia, while the Russians and Chinese push back on Eastern Europe.

Verdun is a border town of France near Germany, south west of Luxembourg. Based on the map in the General office, it's several hundred miles into the Mimic controlled Border. It would not be a strategic point based on current territory projections. It would be dumb, plainly speaking, to launch an offensive there when they are losing the war, and it was only through Rita's looping they seem to win, later shown to be allowed to win.

And since based on the map, it's still significantly in enemy territory, the battle was never to keep territory, likely a strategic, low casualty withdraw, that was spun to encourage humanity. Considering that Cage is a military PR Spin Doctor, in movie, the location is coincidence, and not supported by on screen facts.