I should add a small update here.
First, the Ampcom AM3A-SFP-10G-T module actually works great and the issue was discussed in detail here. TL;DR: I did not pay attention that a bridge device had not included the ports for the SFP slots. Updating a device by simply adding the necessary ports fixes the issue.
Second, I had no luck with TP-Link TL-SM510U SFP module. It is recognized, but doesn’t work either with Ten64 or a switch. Not sure if it’s broken or it’s some type of SFP I do not understand, but suffice to say I’ll stick with Ampcom / FS.com modules for now.