Yes. I resisted going that far in my suggestion, sensing that George's grandmother would not approve. There are advantages to throwing an Arduino or an ESP32 into the mix, though. In addition to the protection-via-timing technique you describe, the limit switches are reduced to signal devices passing negligible current. Magnetic reed switches work fine. There is no high-current circuitry except from the actuators to the H-bridge. Plus, of course, you can program added features, such as "tap to close completely" and so on. This was important in my setup, since I have two sides to control and they need to be continuously positioned in "reclining seat" mode. Also, I have two extra little actuators that "pop" the flat bed upward to get the fold started.
George's situation is simpler, so the tradeoffs are less compelling.