Have to agree with Thunderbolt - love BattleTech because it makes me think.
That being said, maybe the Jumpsail/KF drive likes only a specific radiation wavelength? This is contained in the solar wind at the jump points (and throughout the star system) and is absorbed at the usual listed rates. However a recharge station can broadcast at precisely this frequency, allowing for faster recharge times.
It might also account for the different recharge times at different star types.
I don't see that working. A big reason why sails shrunk over time is that they now drink in a much wider variety of EM radiation to use as "fuel".
If you want to explain things then you can't rely on just the 100% canon information. You need to extrapolate and bring in mew concepts that work within the existing rules, or at least, as much as possible.
For example, my own "headcanon" runs like this...
We all know the basics of the jump system...it is described in books.
It uses Germanium. More specifically, it is the rarest isotope...Germanium 76...which is of value. Why? Because it is radioactive.
More...because it so Germanium, it is transparent to IR light.
2....a jump process requires the core to hold about 130MWh of power. That's a fair amount, but nothing a diesel generator cannot produce in a couple of days. Heck, it should be possible to simply trickle feed the core from the existing power systems.
Why use a sail? Several reasons.
Early jumpsuits used a power plant. It was heavy enough that it reduced the jump radius by more than half. Why would such a generator be so heavy? Because it isn't the amount of energy that is important....it is the density (for lack of a better word). The drive doesn't care where the power comes from....but what it does need is enough power to spark the jump. What the core and storage system does is allow the system to carry enough power so that it can be dumped into the system in a nanosecond.
That 130 or 200 or whatever MWh then becomes equivalent to an energy output of 130 PetaWatts or more. Only for a fraction of a second, but it is long enough to initiate the jump process. You could posit more power is required but that this may be drawn directly from KSpace itself.
3...The act of jumping creates a KF field around the core. The more power pumped into the field, the longer it can be stabilised for a jump, and the longer it is stabilised, the further it can be jumped. But, the more power pumped into the field then the more unstable the field becomes...a spring too tightly wound...and the more vulnerable it becomes to outside interference. A misjump happens when the field twisting becomes so severe it causes the field to break.
4...The outside "interference" is represented by our old friend in the BTU...Heat. Just as 76Ge is transparent to IR radiation, making it a necessity for jump drives, heat inside the jump core can interfere with the jump field. Thermal Poisoning of the Core is to be avoided. This is why Quick charging uses so much reaction mass....it isn't being burned. It is being flushed through the core to keep it cold and then any that can't be cooled quickly enough is thrown over the side. It is dumped. Any JumpShip seen with a bloom of reaction mass around it is dumping the fuel too hot to use in the core or even keep. But quick charging, regardless of source, still entails the risk of thermal toxicity, the risk of creating heat nodes within the core that will warp and twist a KF field.
This need to avoid the thermal contamination of the core is also why more advanced superconductors aren't used...the liquid helium is necessary to keep the germanium cold enough for the jump process, so it simply saves mass by doing a double duty as coolant and battery.
5...One other factor to consider is that the creation of a KF field leaves a charge upon the core. Jumping with this charge is dangerous as it interferes with the KF field. It is almost akin to jumping with a second core, not quite as destructive but still risky. Discharging the charge is dangerous and can damage the ship, a bit like static electricity and it effectively grounds the field into the KF core, equalizing the KF potential. Most jumpships prefer to let the charge dissipate naturally over the course of a week unless absolutely necessary.
The LF battery system includes mechanisms to help dissipate the charge but still only doubles the discharge rate.
So....the sail replaces a heavy generator because the sail includes mechanics to boost the energy density to a point the jump can be sparked. This process doubled the range by removing the generator system but it didn't speed up the jump process because discharging the KF Potential of the vessel....shall we call it shimmer heat?...takes about a week due to safety. The sail system was built and designed with this limit in mind. However, moving to the sail also introduced the problems of thermal toxicity within the core and did little to negate the issues of field twisting.
Now...this expands upon the existing info, but adds concepts and systems that aren't fully canon. But it mostly works, even if it adds s couple of minor issues.
But within canon itself, the jump process, quick charging, core construction, etc have a number of built in paradoxes that simply need to be accepted. Would tbe concept that the drive requires only a special frequency if EM light work? Maybe, but then you are drawing in even less power, and contradicting other information.