Feel your pain with the scope being to short. 2-7x is by far my favorite hunting magnification but I too have trouble getting them onto my long action guns. Most of the time I have to step up to a 3-9x. You should be able to find a one peice base that will work for either gun but if it's like around here you won't find em locally.
As which gun kinda depends on terrain. The .270 will do fine (although I don't like em. They are like butt holes, everyone's got one) with game bullets but I don't like shooting big centerfies in populated areas where ricochet may be an issue. Even the varmint bullets for em are too heavily constructed IMO. Use the .243 and you can limit the issue a little with bullet choice.