You have understood the trade correctly, and then overestimated one side of it. Drawn comb is genuinely valuable, and at your scale it is not worth an extractor.
What the trade actually is. Drawing comb costs the colony a lot of nectar and a lot of bee-hours, so an extracted frame handed back is a real head start — the colony can fill it immediately instead of building first. Crushing destroys that. In a big operation, over many boxes and many years, that difference compounds and pays for the machine.
With one hive, it does not. Seven frames a year of rebuilt comb is well within what a healthy colony does during a decent flow without noticing much. You are trading a modest amount of colony effort for several hundred in equipment that sits in a shed for the other eleven months.
Crush and strain, practically. Cut the comb out into a bucket, mash it, and let it drain through a coarse then a fine strainer overnight in a warm room. That is the whole method. Warm helps a lot; cold honey barely moves.
What you get back. Wax, which is the part people forget. Seven frames of comb is a real quantity of wax — worth rendering, and it has value or use of its own. Counting that, the exchange looks better than the bare comparison suggests.
One caution: strain more than you think you need to. Fragments of wax in the jars are the usual first-year disappointment and they are entirely a straining problem.