I do not think the H is being patronizing when he says that OP might be bored. Rather, he appears extremely anxious, and that is how OP characterized his frame of mind:

"immediately gets anxious about it "we can't afford that, you'll get bored" etc. and basically refuses to let me quit my job"

I can see how a mention of boredom may be patronizing, in another context, for sure... but in this context, the guy is simply fearful - he has a wife who makes more than he does, who spent years pursuing academic degrees and professional certifications, and who all of a sudden decides that she wants to defect. And he hates his job already - he will hate it even more if he becomes the sole breadwinner, because his anxiety level would shoot up, up, up, and his work performance would go down, down, down from extreme anxiety, and he would hate his job even more for it and become even more anxious, because he would be a poorly performing sole breadwinner... not a good prospect for the H in this situation, I am afraid.

Entrepreneurship is a good idea, but should be worked on while on the job. Of course, it is difficult to combine those two pursuits, but people have been known to do that. Plus, some people who leave their places of employment on good terms later become consultants to their former employers or get leads from them or get networking help.

They also say that being active on LinkedIn helps - it would raise the visibility. I have not tried that, but am just conveying what I have read and heard from many people. Again, it takes time to build up reputation.

So going back to OP: the time Purplepearl spends surfing the web while sitting in her cubicle at work could be used participating in LinkedIn discussions that are related to her profession, or on Twitter. Using anonymous browsing for that would be recommended, as a just in case measure (I do realize that employers won't go after each employee who is browsing the web at work, but still - how difficult is it to get in the habit of browsing anonymously?). In other words, if the main idea is to eventually leave this employment and work for yourself, there is a lot of prep for working for yourself that can partially be done at work, in place of surfing the web. None of those options is easy or offers a free ride, but they are doable.