I would temporarly fasten some guide blocks around the bore to get lined up. The issue will be keeping it from getting cocked, if You ever used a Volkswagen jack from the '60s, You know what I mean. A smooth lead in radius on both parts is a good idea, even if it is small. If it were up to Me I would rather work at room temperature and use lubrication than at low temp and dry, and I would use blocking and jack screws to keep it going in evenly. From Your desctription it seems the OD of the ring and the ID of the other part are bearing surfaces, and You need to keep them from getting marred. By the way, I think the figure I gave last night is way wrong.
update: we got the ring in place today, had 2 to drop in, 1 going 3.5' down and the other is at the top, we made a tub for soaking the ring in nitrogen, and a spider to keep it round, also the spider was made to be adjustable in size to shrink with the ring. we got a total of .5 inches shrinkage through the Diameter.
we had porta-powers in place in case of a jam, but never needed them. we got the temp of the ring to -200 before moving out of tub. posting a couple pics.
Glad to see that it worked.