About your question:
Would it be better to disable the charge if the panels can't provide the power required to satisfy the set current (like an on-off control scheme)?
I agree with Filek’s short answer: Do NOT DISABLE the charging.
Battery chargers use the Constant Current limit (CC) during the Bulk charging phase, but that is considered an Upper limit, associated to the battery size and battery capacity to receive current and convert into electrochemical charge.
A classic 3-stage battery charging system is shown as here (adapted from here):
However the power from a Photovoltaic “PV” panel is not constant, and varies with the amount of instantaneous solar power available.
Researching commercial Solar Charger controllers, the user manual of this one from Schneider Electric, brings useful information, per following pictures - about MPPT tracking:
And about the 3-stage charging method being used as a reference, but the blue boxed text shows the actual charging parameters depend of Solar power availability:
I also found a remarkable source of information about MPPT and CC-CV algorithms and methods for a smart asynchronous buck-converter and MPPT controller, entirely made by TechBuilder and shared on a Instructables page. The downloadable PDF version has 156 pages and there is also a video showing the design & construction of the MPPT Charger, that I recommend to be seen before the reading.
Inside the TechBuilder’s project, he mentioned he developed the variable charging algorithm using his modified version of “Coulomb counting” method.
I also found two articles discussing and reviewing different techniques of MPPT and monitoring the State-of-Charge “SoC” of batteries. The links are here and here. It gave me a better understanding, not commercially biased, of existing SoC and MPPT techniques.