Conclusion: Ultimately, this is NOT the best way to make a pulse charger. (Design too simple, compromises too complex. ) 1st make specs for input and output pulse current, rise time, duration. The best simple way uses the battery itself to make negative spikes then a simple battery charger to make up the 5W to 500W you choose for desulphation rate.
You have something that works with a similar efficiency of any unregulated bridge diode-RC charger with a lot of low rep rate (100Hz) line pulse noise too. It ought to pulse at 20k to 50kHz rate with microsecond pulses and current depends on design but with 100W rapid and 5W maintain desulphation without acid electrolyte evaporation at > 14.2V. Basically, as we heard from an investor who wanted to buy my client's patent for $1m, they had a blow torch but once trigger auto accelerometer sensor airbags nearby, we had a Bic Lighter that worked using only 5W to trigger sulphate crystal breakdown from harmonics.
I see better that you know what you are doing. Newbies, do not try this yourself without details on each component. Risks of doing it wrong are severe.
The bulb characteristics are 1:10 R ratio e.g. 10 to 100 Ohms (cold to hot) at rated power but heat rise time and cool delay time affects the pulse characteristics of this bulb pulse SCR charger. In some ways, the bulb heat modulation with the diodes mimics a "PTC semiconductor", current limiter, but not efficiently.
Conclusion> The only way to improve efficiency is to reduce ESR of expensive caps and insert bulky ferrite core very low DCR coil (LC filter) to reduce current and store energy. That is how Buck regulators store energy.
Reducing bulb resistance is the only way to reduce losses but that affects pulse width and current so they run cool.
This is my sim. You must change the values to your model.
My switch allows you to charge an 11V ideal voltage source with battery capacitance with a 1.3V charger using a modelled convenient rapid (fake) charger)
I support the theory and practice of pulse de-sulphation for. My former employer used to manufacture them and I verified the design and I know someone with 20kHZ 300A ??ns pulse battery rejuvenator that works extremely well.
* obligatory warning for readers*
This work ONLY for proven experienced technical people that understand battery and Cap ESR and that a short-circuited battery cell fuming hydrogen can be dangerous.
I cannot optimize your design, off the cuff, without these characteristics. But with this tool and your actual model, you might.
You can even change the battery 10mOhm ESR with an ideal pot of 100mOhm value and adjust it.
I've done a similar thing in my past life ;) in Winterpeg, Manitsoldhere, Canada with cold dead batteries and not having a charger at the time in the late 70's and even later.
To reduce 120V/60Hz to12V means I was 10% efficient so I used a 1500W toaster in series with "HOT" = Line1 120V. It got me to work on time in frigid weather. After a toaster, I used a single 25A diode in a glass of snow after the ~100V voltage drop with a careful connection of my neutral (near 0V earth) to chassis ground.
At least I could heat a bagel while waiting 10 minutes to get enough charge to start the engine.