My impression is that mature Unix-like operating systems are less vulnerable to trojans that might be present, mainly because of well-debugged kernel code, including correct use of hardware memory protection. Is that correct?
No. THe primary reason that there are less known vulnerabilities for mature Unix-like OSs is that they are fewer individual systems running them, and the systems running them tend to be less exposed to external threats. That means that few security researchers and adversaries have incentives to find vulnerabilities.
Notice that fewer known vulnerabilities does not mean there are fewer vulnerabilities than Windows or Linux systems, just that no one has spent the time or effort to discover them.
Is any company or group known to be working on hardware architectures aimed at preventing vulnerabilities from application code -- even if the OS is not Unix-like, and even if trojans are present?
Hardware protection mechanisms are not good at discriminating between system software and and application software. That is typically the realm of an Operating System which knows the hardware capabilities of a system and grants resources to application software. The closest well known hardware example might be ARM's Trust Zone (http://www.arm.com/products/processors/technologies/trustzone.php) which provides an additional hardware protection layer on given processors, but still requires software to play a role in handling hardware signaled events.