Power supply voltage clamp
Looking for an efficient solution since the solar panel can only
produce 500mA max and I want as much of this to be used for charging
the battery when it's available.

Use a buck-boost pre-regulator like this one from Analog Devices/Linear Technology: -

You can work this from any input voltage in the range 2.5 volts to 15 volts. Texas Instruments will no-doubt have similar offerings. If you need a bit more power (and efficiency) then consider this one: -