Two miles* tall? *
That’s what the article I linked to said but the Wikipedia article on the Laurentide Ice Sheet (95-20,000 years ago) says, “It was up to 2 mi (3.2 km) thick in Nunavik, Quebec, Canada but much thinner at its edges where nunataks were common in hilly areas.” So I’m not sure how thick it actually was in the tri-state area.
The thickest ice in Antarctica is 4776 meters(15670 feet) -just short of three miles thick. The weight of it has caused the land it sits on to become below sea level.
It’d be easier than that. Just boost up into an orbit with perihelion at 1 AU and a period of 1.5 years. Or boost into an orbit that’s just slightly above or below 1 AU, re-circularize your orbit, wait for Ærth to catch up, and then boost back down. Heck, if you want to take the scenic route, you could go via Mars, which would be exactly as difficult as, well, going to Mars.
I think you are telling us: there is such a planet, and we should look for it, Spaceman. I am lackadasical and think “there’s plenty of time”. But it doesn’t matter what I think: I am just a yokel. Too bad we can’t get past the darn “Van Allen Radiation Belts”. Nasty gamma rays…
We can’t even rebuild Puerto Rico. 
How thick were the glaciers that moved over North America?
Sure, beyond the energy required to escape Earth’s sphere of influence, you can pick a minimum energy trajectory for any given period, but then you are going to have the crew exposed to cosmic radiation beyond lifetime allowable levels and the potential of solar particle events, as well as having to provision for that period to maintain a closed habitat. Given our current experience with artificial closed ecosystems and the psychosocial problems with small groups in confined environments, minimizing the duration spent in transit would be important, notwithstanding that we currently do not have the capability to launch or assemble a spacecraft of size for colonization.
I’m not sure if this a whoosh, but the Van Allen belts are zones of concentrated charged particles from the Sun captured in the Earth’s magnetosphere, not gamma rays. The simple solution to protecting a crew from the effects of the Van Allen belts is simple; pick a trajectory that does not pass through the most dense regions. Coronal mass ejections and high energy cosmic radiation are still of concern, but the former can be mitigated with shielding and the latter by minimizing the time spent in transit, or with future innovations in molecular biology, augmented repair mechanisms for cellular organelles and the genome to fix radiation damage.
Stranger
We’d need to be careful, the government there might not be what we’re used to.
I meant the gamma rays will get us if we go beyond the protective van allen radiation belts.
Still wrong. There are high energy gamma radiation primarily from supernovae and X-ray binaries, but these are infrequent and dispersed enough that they don’t pose a statistically significant hazard. It is the massive charged particles that do more damage due to their higher energies and tendency to not only interact with astronauts and other mass of a spacecraft, including any shielding, but to also produce a spray of secondary unstable particles from those interactions that decay into ionizing radiation, extended exposure to which causes cumulative cellular and genetic damage the effects of which are becoming more apparent to space physiologists. In any case, it is not the Van Allen belts that protect against this cosmic radiation but the thick atmosphere of Earth, and exposure to cosmic radiation is tolerable for a limit duration as demonstrated by the Apollo missions and the extended stays in the International Space Station.
Stranger
The Trojan asteroids (the ones at the two Lagrange points) are actually not so small in terms of total count. The estimate I’ve seen recently is about the same number of rocks as the main asteroid belt. There’s less total mass among the Trojans, because the largest (which have most of the mass) are significantly smaller.
There is another way you could get another planet in the habitable zone besides the unstable far side of the Sun, a double planet, or an extra-cold planet (larger Mars). Two planets potentially could be co-orbiting, like Janus and Epimetheus, two satellites of Saturn. Granted, it’s not too likely that large planets will fall into such a configuration, but it’s certainly a possibility. And before you ask, it’d have been naked-eye visible, so there’s no way we wouldn’t have seen it. In fact, at times it would have been the brightest thing in the sky except the Sun and maybe the Moon.
There certainly has been such an ecosystem. During the last interglacial period, some 95,000 years ago.
Random extinctions did happen without humans being involved. The most famous example would, of course, be the extinction of the dinosaurs. You might have gotten huge herds of bison in North America if humans had never been there, but on the other hand it’s possible that something else would have killed them off.