Surprised noone's suggested it yet. If you're willing to do a relatively simple pin mod, you can do away with the Lin Lin adapter and run a Tualatin directly in a Coppermine slotket.
If your mobo or slotket allows setting the voltage manually with jumpers or from BIOS menu, you don't even need to do the VID part of the mod (the blue/purple pins), and get away with desoldering two pins and isolating/bridging one. I did the latter by cutting the trace to the AK4 pin and soldering in a jumper wire to AN11.
I've done it successfully with a couple of MSI MS-6507 Master slotkets and one called 370SPC from an unknown maker. The former has VID jumpers, the latter is used with an Abit BH5 mobo which allows setting the voltage from BIOS. Maybe those relatively modern slotkets even will forward the VID signal from Tualatin processors correctly and would work with auto voltage setting without doing the VID part of the mod. Haven't researched it though, setting it manually was good enough for me.
Note that the CPU VRM on the mobo of course must support the voltages you want. That seems to be one of those mixed bags when it comes to Slot1 mobos, it can even vary between different specimens of the same model. You'll have to find the datasheet for the VRM controller found on your board and look it up.