One alternative would be to use an external Composite decoder/comb filter to convert the Composite video signal to S-Video (or YPbPr/RGB if you're also modding for those inputs), but those devices are specialty devices that can be hard to obtain nowadays. Another alternative would be to use an S-VHS VCR with an S-Video output for a Composite comb filter. DVD recorders with S-Video outputs and Composite video inputs do exist, but those a) are pretty expensive to acquire, b) digitally process the signal, resulting in input lag, and c) treat 240p signals as 480i. Therefore, a DVD recorder (or DVD/VCR combo recorder) is not an ideal device to use for this purpose when hooking up a Composite video game console.
Ideally, it would be best to have the Composite video input signal filtered outside of the jungle chip, bypassing the need to use an external comb filter or service menu. Luckily, there were a few models (including the KV-20V80 and a few PAL region models) that used an internal comb filter chip to handle Composite processing. I'll be covering how to install this comb filter into the models without one, that way if you intend on S-Video modding the set, you won't have to deal with the usual drawbacks whenever you wish to use a Composite video device.
WARNING: Most of the components you will need to solder are surface mount components, therefore this tutorial should not be performed by beginners. If you don't have experience with SMD soldering, please practice on less sentimental PCBs (i.e. from broken electronics) before doing this to your TV.
Here's a list of components you will need to install (expand Spoiler to view):
Spoiler
FB350, JW120, JW121, JW302, JW380, JW390, and JW393 - Jumpers
C307, C351 and C362 - 10uF 50V Electrolytic Capacitors
C348 - 330pF 50V 0805 SMD Capacitor
C350, C352, C357, C359, and C360, - 0.01uF 50V 0805 SMD Capacitors
C353, C354, and C356 - 0.1uF 25V 0805 SMD Capacitors
C355 - 0.22uF 25V 0805 SMD Capacitor
C358 - 47uF 25V Electrolytic Capacitor
C361 - 0.022uF 50V 0805 SMD Capacitor
IC302 - CXD2073S
Q350, Q352, Q353, Q354, Q356, Q357, Q359, and Q380 - 2SB709A-QRS-TX transistors (BC807 is the modern equivalent)
Q351, Q355, and Q358 - 2SD601A-QRS-TX transistors (BC847B is the modern equivalent)
R350 and R351 - 220 ohm 1% 1/10W 0805 SMD Resistors
R352 and R354 - 3.3K (3300) ohm 1% 1/10W 0805 SMD Resistors
R357 - 56K (56000) ohm 5% 1/10W 0805 SMD Resistor
R358 and R362 - 560 ohm 5% 1/10W 0805 SMD Resistors
R359, R367, and R380 - 2.2K (2200) ohm 5% 1/10W 0805 SMD Resistors
R360 - 22K (22000) ohm 5% 1/10W 0805 SMD Resistor
R363 - 330 ohm 5% 1/10W 0805 SMD Resistor
R369 - 680 ohm 5% 1/10W 0805 SMD Resistor
R353 and R370 - 0 ohm 0805 SMD Jumper Resistors
R372 - 270 ohm 5% 1/10W 0805 SMD Resistor
R378 - 470 ohm 5% 1/10W 0805 SMD Resistor
R361, R376, R377, and R379 - 1K (1000) ohm 5% 1/10W 0805 SMD Resistors
R366, R375, and R382 - 1.5K (1500) ohm 5% 1/10W 0805 SMD Resistors
R303, R364, R365, R368, R373, R374, R387, R388, R395, R396, and R397 - 100 ohm 5% 1/10W 0805 SMD Resistors
L351 - 47uH SMD Inductor
L352 - 10uH SMD Inductor
C307, C351 and C362 - 10uF 50V Electrolytic Capacitors
C348 - 330pF 50V 0805 SMD Capacitor
C350, C352, C357, C359, and C360, - 0.01uF 50V 0805 SMD Capacitors
C353, C354, and C356 - 0.1uF 25V 0805 SMD Capacitors
C355 - 0.22uF 25V 0805 SMD Capacitor
C358 - 47uF 25V Electrolytic Capacitor
C361 - 0.022uF 50V 0805 SMD Capacitor
IC302 - CXD2073S
Q350, Q352, Q353, Q354, Q356, Q357, Q359, and Q380 - 2SB709A-QRS-TX transistors (BC807 is the modern equivalent)
Q351, Q355, and Q358 - 2SD601A-QRS-TX transistors (BC847B is the modern equivalent)
R350 and R351 - 220 ohm 1% 1/10W 0805 SMD Resistors
R352 and R354 - 3.3K (3300) ohm 1% 1/10W 0805 SMD Resistors
R357 - 56K (56000) ohm 5% 1/10W 0805 SMD Resistor
R358 and R362 - 560 ohm 5% 1/10W 0805 SMD Resistors
R359, R367, and R380 - 2.2K (2200) ohm 5% 1/10W 0805 SMD Resistors
R360 - 22K (22000) ohm 5% 1/10W 0805 SMD Resistor
R363 - 330 ohm 5% 1/10W 0805 SMD Resistor
R369 - 680 ohm 5% 1/10W 0805 SMD Resistor
R353 and R370 - 0 ohm 0805 SMD Jumper Resistors
R372 - 270 ohm 5% 1/10W 0805 SMD Resistor
R378 - 470 ohm 5% 1/10W 0805 SMD Resistor
R361, R376, R377, and R379 - 1K (1000) ohm 5% 1/10W 0805 SMD Resistors
R366, R375, and R382 - 1.5K (1500) ohm 5% 1/10W 0805 SMD Resistors
R303, R364, R365, R368, R373, R374, R387, R388, R395, R396, and R397 - 100 ohm 5% 1/10W 0805 SMD Resistors
L351 - 47uH SMD Inductor
L352 - 10uH SMD Inductor
Here's the comb filter schematic for the KV-20V80 to illustrate this circuit (click the image for full resolution):

On the BA-4D chassis models (Models ending with 42/43/52/53/90), there's an optional buffer circuit for the video input to the comb filter chip. Whether you want to use this or not will depend on if you're shorting SMD resistor footprint R340 (connected between pins 4 and 5 on the chip):

If you choose to keep R340 open, populate the following components:
C340 - 1uF 50V Electrolytic Cap
Q340 - 2SD601A-QRS-TX (BC847B is the modern equivalent)
R341 - 47 ohm 5% 1/10W 0805 SMD Resistor
R342 - 100K (100000) ohm 5% 1/10W 0805 SMD Resistor
R343 - 10K (10000) ohm 5% 1/10W 0805 SMD Resistor
R344 - 3.3K (3300) ohm 5% 1/10W 0805 SMD Resistor
Otherwise, short R340 (either with a solder blob or a jumper resistor) to use the comb filter's internal clamp.
On my first attempt at this mod, I mistakenly shorted R340 and installed the aforementioned components for the buffer circuit, the end result was that the image was either in black and white or with a blue emphasis. What I did to compensate was I replaced R350 with a 680 ohm resistor, which resulted in the color tint being shifted, making it necessary to adjust the tint when changing between S-Video and Composite/RF. If you happen to make this mistake when performing this mod, remove either R340 or R341 depending on which clamping circuit you wish to use.
Before installing the chip, there are seven jumpers that you will need to populate, one of which (JW302) goes underneath the chip, so it is preferable to install this jumper BEFORE you install the chip. Below is a photo of the jumpers you need to install:

Unfortunately, I didn't take photos of the board as I was performing this mod as I didn't think to take them, but if you pay attention to the component labels, where they connect, and the arrows they point to (for components whose labels are far away), you should be able to tell what goes where. All SMD components should go to the bottom side of the board (the green side, in other words).
After you've installed all necessary components on the board and reassembled the TV, go into the service menu by pressing "Display", "5", "Vol +", then "Power" on your remote, then change the following settings accordingly:
- Set CTRP to "1".
- Set CBPF to "0". (Recommended to reduce color bleed if modding for S-Video.)
- Set SHPF to "1".
- Set FSC to "1". (IMPORTANT: This activates the Oscillator output from the Jungle Chip to the Comb Filter Chip. If you forget to change this value, you won't get a picture as the Comb Filter won't function without it! I've learned this the hard way when I first performed this mod.)
- Set ID-1 to "19". (If you intend to S-Video mod the set. Set to "17" for the KV-13M40/42 as that model only has one Video input.)
- Set ID-4 to "31".
I currently don't have any "before and after" photos of the mod, as I forgot to take them, but the end result should be a sharper Composite picture with reduced dot crawl artifacts and consistent quality across your different inputs (i.e. S-Video will no longer interfere with Composite).
That aside, hopefully this helps anyone seeking to perform an S-Video mod on a smaller BA-4 chassis Sony TV or anyone who just wants a less noisy Composite picture.