OK, as a certified pilot, I'll try and clarify.
In general, Pilot certificates do not have expiration dates. However, the rules build in a check that needs to be maintained every 2 years for continuous currency - but you could lapse and say take a number of months break and then get recurrent by completing the recurrent requirements.
107.65 governs currency and if you're past the initial, the following applies:
(a) Passed an initial aeronautical knowledge test covering the areas of knowledge specified in §107.73(a);
(b) Passed a recurrent aeronautical knowledge test covering the areas of knowledge specified in §107.73(b);
So, the critical thing here is the wording "knowledge test" - yes, that's defining that it's something to be completed at an FAA testing center. I don't see any leeway (unless you have a pilot cert issued under part 61) in there for a "company approved program" - it's clear that it needs to be a knowledge test.
Now, 107.73(b):
(b) A recurrent aeronautical knowledge test covers the following areas of knowledge:
(1) Applicable regulations relating to small unmanned aircraft system rating privileges, limitations, and flight operation;
(2) Airspace classification and operating requirements and flight restrictions affecting small unmanned aircraft operation;
(3) Emergency procedures;
(4) Crew resource management;
(5) Aeronautical decision-making and judgment;
(6) Airport operations; and
(7) Maintenance and preflight inspection procedures.
Now, I just looked and I don't see a "recurrent" knowledge test. However, by default, the recurrent is a subset of the initial.
Just as a comparison, as I am a Part 61 certificate holder, the test I have to do is a "training course" which is available through the FAA training website (faasafety.gov). Now, again, it doesn't seem like there is any recurrent course, so I'll likely do the initial again......
Hope that helps,
John