For L1 just put a zero ohm link in its place. The ferrites inline with the signal are pretty much only there for EMI compliance.
In fact a quick and effective fix for cards with muddy VGA out (I've done it myself on a couple of ViRGEs) is to jumper the ferrites and remove any caps between the video signal and ground.

As for the other caps I feel like you can't go wrong with 100nf.

Do you happen to have some scrap cards you can salvage for parts? then use the closest parts you have. For the resistor networks, for example, 22 or 47 ohm will work just the same.

So, made some progress!

That L1 was replaced with a wire, I have refitted the loose resistor and soldered back the capacitor at C113. The biggest challenge was the resistor array, which I decided to replace with 4 individual resistors that I salvaged from some junk cards. The caps - I just took some from other cards, near memory, a blind shot. Also, my friend borrowed me a JBC micro soldering station with insanely small tips, making the work easier.

The card boots, however the image is a mess 😒

I am thinking of reflowing the card since when I put pressure on the heatsink the pattern changed, THIS video shows a good guidance as to how to do it. However, I cannot take the heatsink off. Tried heating it with heat gun (with around 130 deg temperature), tried freezing it with upside-down compressed air spray, but the heatsink won't move an inch. Any ideas how to take it off without damaging the chip?

Forgot reflow, go for reball, this card is worth additional effort. But first check all ladder resistor packs 4x33ohms, especially the blue ones - in other card I had to replace 25 pieces due their resistances floated from hundreds ohms to several kilos. Their values should be in range 22-56 ohms, but best if nominal. Measure each of any of four and if resistance is wrong, then just replace from donor board, they often exist in motherboards. Check again for broken small smd parts and replace if necessary. Also replace all 5 inductors Lxx near vga socket from donor to be same, do not left wired one, there are rgb and h/v sync signals. Check also with nail all legs of sgrams, it's possible that one or more have bad contact/floats. To remove heatsink just use hotair and remove it by horizontal twist, never lever it vertically coz you may damage pads under gpu. Good luck.