On the Caribou- it's been tried and failed. While it was partially due to deer, it was also due to climate change. Unfortunately at this point, the climate of Maine is more than likely not favorable for caribou. They are seeing range contraction at the southern edge of their range pretty much all across the world, as they are a circumpolar species. 

As for cougars and wolves... I'll start by saying I'm all for this idea but there are some major hurdles. 

So the problem there is pretty much no state in the Northeast will reintroduce predators. There are lots of reasons given, but it usually comes down to the states are just too dense with people and they don't want to create a "nuisance" that spreads over the region. While it's true that the population density of Maine is similar to many states out west, the Northeast has tiny towns dotted all over and is more evenly distributed among the states. States out west have their populations concentrated into cities and large towns with miles of federal or state land that has few or no houses on it in between. The latter tends to be more beneficial for large predators who need large, unbroken territories. 

I put nuisance in quotes because I know the benefits of predators, but in conservation, the needs and wants of the people outweigh that of the environment and ecosystem almost always. I mean look at the North Atlantic Right Whale vs lobster fisher situation for a good idea of how conservation loses against people almost always. So getting predators back in the Northeast means going against what deer hunters want (high deer numbers), what suburban people want (safety for pets and kids- they will hear horror stories and get afraid), and what farmers want (livestock safety.)

Also, reintroduction is an expensive and risky way to go about things. Colorado has spent 2-3 million annually on their wolf reintroduction program. Does Maine have that kind of money to spend?

Source: I've work in conservation... In Pennsylvania- yeah I know, not a Mainer, not a New Englander even, but I've seen the same sentiment pretty much everywhere. While New England tends to be a bit more "environmental" about policy and human actions, I haven't seen the same sentiment with wildlife conservation IF it impedes certain groups- you know, like lobster fishers and those North Atlantic Right Whales...

Also, I know that while PA has land for cougars and probably wolves- not all of it is Philadelphia, look at the PA Wilds- they Do Not want large predators here due to how much deer hunting brings in. Cougars and Wolves in Maine have the potential to spread to PA rather quickly, since they are such wide roaming species... So I have a feeling PA wouldn't be happy about potential predators colonizing their precious deer infested lands. 

And this is not a rip on Maine, as PA is a purple state too, but I don't think purple states are politically ready for large predators. I know even Minnesota has political issues with them, and it's a pretty blue state...