However, I want to defend the idea that some right wing opinions make a lot of logical sense on their own; their being valid does not require right-wing-specific value systems.
Let's take one of the points you're criticizing.
> someone who doesn't work and doesn't contribute to society doesn't deserve govt handouts
Here's the logic: the products and services we enjoy every day are all the product of someone else's work. None appear out of thin air. If they're provided by the government, they are still funded by taxes on the fruit of someone else's work. Why would someone who does not produce anything be entitled to any of it? The basic value behind this point is plain fairness, which everybody agrees on.
That being said, I will concede the above point needs refining and nuance before it can be used as a principle to guide public policy. For instance, it makes sense that society should help people who cannot work because of some handicap. The value here is common decency, which is neither specific to the right or the left.
Another refinement: what about people who are out of work and haven't found their next position? It's probably productive to help them with unemployment benefits: we can bet they will be back on their feet faster if they worry less about immediate money problems. The value here is efficiency. Of course, these benefits should be delivered under certain conditions, because the overall point regarding fairness still stands. They are not entitled to the fruit of someone else's work if they refuse to give back.
So here's the refined point:
In a fair society, people who are able to work but willingly refuse to do so should be not entitled to the fruits of someone else's work. However, people who are unable to work, whether permanently or temporarily, are excluded from this point and may be helped through the means of redistribution.
The final point is maybe a bit centrist, but still fairly right-leaning in its position. It's very logical, and only buttressed by the shared values of fairness, efficiency and common decency.