Am I being penny-wise and pound-foolish by not wanting to spend four-hundred dollars on online course software?
Having had to cope with these questions myself, might I suggest taking smaller steps first? You could begin with a simple mini-course available for free or very low-fee (say $19-$29), one that solves a common but acutely felt problem that exists with your audience, and would be a great next step for solidifying your relationship with your book readers, website visitors, etc. Think about what you could realistically design and deploy in the first month of membership. Just throwing out ideas, but for example you could:
Give yourself 1 week to prepare the mini-course. Choose your topic, split into 3-7 sections. Write or film them. One of the cognitive tricks I use for developing content is to imagine what an extremely detailed 1-page worksheet or assessment would look like turned into a series of video topics. We don't tell them what to think, we just show them a framework for how to think, and they supply the answers themselves.
Then give yourself another week to get everything set up on teachable.com. Configure your school. Upload your course content. Setup some Drip emails to keep them engaged in completing the mini-course.
Use the remaining two weeks to incorporate your mini-course offer into your outgoing messaging (forum posting, email signature, social media profiles, etc.) and relax!
Taking into account your timing, I'd say right now is a great time to start! You could have it all ready by the time your book comes out, especially if you are a confident content creator. A couple of sales between now and then would at least offset the hard costs, but might even turn a profit. If you choose to offer the content for free to book buyers, teachable.com is still a magnificent way to store your content and manage access to it. You can still give it to your book buyers for free and charge the public full price. Just create a 100% off coupon in teachable and make sure it gets to your book buyers.
Since you got my gears spinning, here's some mini-course ideas for you:
5 Keys to Keeping Smart Kids Interested and Engaged In Learning (each day of the course goes into one key in more detail)
5 Math Shortcuts They Don't Teach In School Anymore (Heck, you'll probably get some adults buying this for themselves!)
5 Impediments to Finding Joy In Writing and How to Overcome Them