Charles,
I agree with some of what you posted and disagree with some. The most important part that I don't really care about is the Republican Party. The party left me a long time ago. There are large groups of people the Republican party needs to appeal to if it wants to survive and prosper. Hispanics are one, Blacks are a second, and the libertarians (note the small "L", this is the people who hold a philosophy and not the party members particularly) are a third. All of these groups have things in common with the GOP and all have differences.
With one caution, I would say the GOP needs to really carefully examine its platform and plans. One of the few good things I see in the future for the GOP is the fact that the Democrats are a party of alliances that will fracture apart. There is no true Democratic core belief. Instead, there are alliances between extreme core beliefs from several different groups, such as the socialists, the environmentalists, the animal rights groups, the peace at any cost groups, etc. I think it will break apart under the stress of trying to govern. If the GOP tries to become a similar coalition party, it also cannot survive.
What I think most people really want to see in the US, and the GOP could pull off with some thought, is a party that fights for fiscal conservation while promoting social liberty. The GOP loses many people when they fight to keep religion in all forms of government. More and more of the country want to keep their own religion and keep it private. The GOP loses when it tries to restrict abortion, especially when it is a restriction based on a religious interpretation. I do not support abortion but I honestly don't think the government should have a say in it. Gay marriage is the same way.
Most people do support gun rights, so the GOP has a draw there. I do hold more extreme beliefs in gun rights than most Americans, but it is relatively easy to fight gun control issues when you prove that it doesn't work for the stated goal.
As you say, immigration is a major issue that the country needs to solve. I am a descendant of immigrants (well, we all are but mine is only three or four generations) and I want to go back to the days of allowing most people who want to come in and work and improve themselves to do so. If we separate the "entitlements" issue from the immigration, I think most Americans want more immigration but do not support giving them any welfare. Argue to stop most (not all, but most) welfare without regard to immigration status while removing immigration restrictions and the GOP could have a winning policy.
Which does bring us to the fiscal conservative part. I think most people in the US could support a policy that helps those who really need it (such as those unable to work) and that provides some benefit to people who need help for a short time. I am sure the GOP could develop a policy that narrows the support over a period of time and ends the generational welfare problem while still providing support for those who really do need help.
And for all of those in here who read this, I want to emphasize that I do not necessarily hold any of these beliefs. Nor do I necessarily disagree with them. My personal beliefs are along the lines of Jefferson's quote about that government which governs least governs best. I do think this type of platform is the one that would have the biggest support in the US population. It would take some demonstrated proof that they really are changing to this way of thought before they see much gain, but then it would come in a landslide. I base this one what turned me off on the GOP, and what I think could bring in the reasonable people from my extreme right side and the moderate to just left of center side people also.
Our country is very divided and now is the time for us to start working on the middle ground. The group that gets there first will control it. The average American does not want to be divided this way.