This answer will change as my research and testing continues.
As of August 12, 2017, I am accepting this as my answer, but I am going to continue to expand on this list as I find new potential alternatives. I still prefer Avast due to its memory footprint and cost effectiveness, but YMMV.
Just to make a note, I did some research based on the amavisd-new package's 15-av_scanners file in /etc/conf.d from the Ubuntu repository and came across Avast and some other solutions. Note that most of the solutions I've found are not free.
Avast Core Security for Linux
While most of the other solutions are not free, I have requested trial licenses for 30 days from Avast for their Avast Core Security Linux suite, which provides the antivirus protection and integration with AMaViS which I required. ($150/year for one server, however there's longer-term-license discounts it seems, with it becoming $295.99/3 years for one server, and varying other bulk-purchase discounts). It's running smoothly with very little resource usage. (~ 5MB RAM consumption on an idle/new mailserver, currently running at ~64MB of RAM consumption after being online for over a month and with handling active mail items.)
They have i386 and amd64 releases of the software. Unfortunately, no armhf or others... but for the average server on standard hardware that one would expect in the average corporate environment (amd64 or i386), it works well and is low-resource-usage.
Note that I went with an Avast Core Security license, as it's the most useful option available to me, balancing server resources and costs as factors.
Sophos Antivirus for Linux
Sophos makes an Antivirus for Linux that is free; you just need to register for it.
In my testing of this, though, I did not see an armhf version, and in working with Sophos for a client, they had told me there's no armhf version when I requested information for their Linux antivirus solution and supported architectures, but they did have an i386 and amd64 version. I also did not dig too deeply into this, because unlike Avast above, the Sophos software is pretty memory intensive as well. While it takes a lot longer to get up to that memory level consumption that ClamAV does, it does eat a ton of memory over time. Tested this on a mail server and it ate the 1GB RAM available to the system in no time, and ate all 1GB of swap while it was at it.
(While this is a free solution, Avast still runs with a lower footprint than the Sophos software, from my testing. Download requires registration (name and email), but is reported to accept even trashmails.com addresses.) Sophos integrates well with Amavis, as e.g. described in this German article.
F-Prot Antivirus for Linux Mail Servers
F-Prot has an antivirus flavor for Linux Mail Servers, which I believe that amavisd can interface with.
I have not tested F-Prot because they do not provide a free version for Linux mail servers ($130 US, for one year, for 1-10 users), and because I could not find a trial version. I've heard of them but can't attest to their usability or usefulness.
