Thicker oil isn't really the answer. It'll slow down how long it takes to dive by a little but it'll still dive just as far.
The budget priced answer for the SV is springs AND thicker fork oil. That should be your first step. Springs are around $200 to $250. Do the springs and oil and you'll love your bike as though it's new all over again. But soon you'll realize that the rear end isn't holding up it's part of the bargain. SO then the trick budget setup is a late model ZX6R shock. It's a direct bolt in. ANd with a bit of patience you can get one off ebay for under $100.
If you can't possibly do the Racetech springs at this time then do the oil but while the cap is off find a bit of plastic or metal tubing that can be used as additional preload spacers and cut off two nice square ended pieces that are 3 cms long. Put these in between the washer on the top of the spring and the top cap. You'll have to push on the top caps harder to get them to screw in. Be sure to keep the pressure consistent for the first 4 or 5 turns of the cap. Then you can use the thread to suck it down.
There's certainly more you can do beyond this. The quick preload fix and even the Racetech springs are just the beginning. THen there's Racetech cartridge emulator valving for the forks. Modified or Racetech valving for the shock. A full Gixxer 600 front end transplant. Ohlins.....
