How should I substitute jalapeño peppers for fresh green cayenne peppers?

I'm not sure you're familiar with it but I'd like to introduce you to the Scoville Scale:

The Scoville scale is the measurement of the pungency (spicy heat) of chili peppers or other spicy foods as reported in Scoville heat units (SHU), a function of capsaicin concentration. The scale is named after its creator, American pharmacist Wilbur Scoville. His method, devised in 1912, is known as the Scoville Organoleptic Test.

Unlike methods based on high-performance liquid chromatography, the Scoville scale is an empirical measurement dependent on the capsaicin sensitivity of testers and so is not a precise or accurate method to measure capsaicinoid concentration. [emphasis added]

This scale is subjective but having many people rate peppers at similar levels gives a pretty decent scale of relative "hotness".

On the scale, the Jalapeño rates between 2,500 and 10,000 Scoville units

It is of mild to medium pungency, 2,500 and 10,000 Scoville units in general.

While the cayenne rates around 30,000 to 50,000 Scoville units:

It is generally rated at 30,000 to 50,000 Scoville units.

It is unclear whether this range includes the immature, green varieties, though some charts place the cayenne at 50,000, so that could give the lower 30,000 as the rating of the green peppers.

So, even at its lowest rating, the cayenne pepper is three times hotter than the jalapeño's higest rating.

Relative hotness aside, I don't believe there's any reason you can't substitute the two. There are two important factors to be mindful of:

• different flavor profile

  Classified, as a hot pepper, Green Cayenne chiles are not as hot as in their more mature red form, yet still offer a pungent heat with a fresh grassy, chile pepper flavor.
  The crisp and juicy flesh of the Jalapeno pepper offers a vegetal flavor and a spicy bite with heat increasing as the pepper peaks in maturity.

• different water content
  • the jalapeno is more wet as it has thicker flesh while the cayenne has thinner flesh. This alone could affect your final product a bit, though you say you cook it down a lot, so it may be less impactful than a fresh salsa.

I'm would not recommend increasing the ratio to 3-1 to make it more hot because I'm not certain that having a higher ratio of heat producing content will actually make it taste as hot as the cayenne ever would - and it will add some volume to your relish. In the end, using jalapenos instead of cayenne will certainly be a different product but that doesn't mean it will be bad.

You can always taste as you go and add more spice before it's finished cooking if the flavor is too mild. Remember, though, that spicy flavors can change as a product ages, the way chili always tastes better the second day.

There are two main factors to consider when you substitute one chili pepper for another. The flavor and the capsaicin level. The flavor of each pepper will have its own unique notes but it will not drastically affect your recipe.

The capsaisin level is the thing to watch out for. A Cayenne Pepper is much spicier than a Jalapeno pepper. A Cayenne pepper will have around 30,000-50,000 on the Scoville Scale while Jalapeno is typically around 3500 to 10000.

It would be unreasonable to substitute 50+ Jalapeno peppers for the Cayenne peppers. But one thing you can do is use the 10 Jalapeno for the flavor and introduce an external source of capsaisin to make the relish spicier.