If that article really is a pretty good summary of Republican thinking in this sphere, then I'd say it completely backs up what I've been saying. There's not much substance in that article. It very briefly mentions the subsidized catastrophic insurance you mention, but it doesn't go into much detail at all. Worse, it completely handwaves away the major problem with that model, namely, what happens to people with chronic conditions, by basically saying "oh well, too bad, so sad."
In any case, I don't see how that approach is ultimately very different. Sure, it means people cover a bit more stuff out of pocket, and places a higher burden on sick poor people, but overall it's pretty much the same.
The ultimate question that has to be answered is this: do we, as a society, find it acceptable to allow people to die of treatable illnesses when they can't afford to pay for the treatment? This question has been solidly answered as "no" in the US for some decades now, ever since hospitals were barred from turning away patients in the emergency room. The question now is simply how you accomplish it.
So, back to these subsidized catastrophic plans. You'll have to have a mandate on them! Without a mandate, people who aren't sick won't buy them unless you hold some other threat over their head, such as denying them the ability to obtain insurance if they're already sick.
Unless we're going to let people die, the wealth transfer you describe has to happen in some way. Pre-Obamacare, it works using a de-facto hidden employment tax whereby better-off people pay, in a really convoluted fashion, for the unpaid bills of poor people. With Obamacare, it works by forcing people to get insurance even if they don't want it. The Republican idea discussed in your link is some combination of the two, and exactly what the combination is depends on the exact details.
Obamacare is just about the most free-market solution for universal health coverage you can come up with. It's more free-market than the pre-Obamacare regime, it was proposed by Republicans, and it was passed by Republicans in Massachusetts just a few years prior to becoming law at the national level. And lest we think that those Massachusetts Republicans were some fringe group, they nominated the governor for President! Why should I expect Republicans to object to it for any reason other than being the political party of Crazy?