There are three big problems with what you are trying to do.
1) once lines have been in service
they harden and become very difficult to splice again. It's possible, but unless the line is very new I flat out refuse to splice Dacron lines. It is possible if you are in the middle of the ocean, but not easy.
2) you cannot taper double braid Dacron lines. Well, you can but in sta-set the load is balance between the core and the cover, removing either cuts the strength by more than half. In addition the outer cover is treated with UV stabilizers the core doesn't. So the newly exposed core will weather
3) doing a constant diameter splice is possible. It's called, surprisingly enough, a Constand Diameter End-for-End splice. But by its nature this splice is dramatically weaker than a normal end for end. I couldn't recommend it for a load bearing application like a furling
line. MAYBE, but I probably wouldn't on a continuious line furler because the line never needs to carry much load, but defiantly not on a drum.
The best answer is to use micro dyneema
for the drum portion of the furling
line, luckily 1/8" amsteel has exactly the same strength as 1/4" sta-set so just switch to that. Of course then you have to have a reasonable tail. Going from 1/8" to 3/8" in one step is going to be an issue, so do it in two. End for end splice the 1/8-3/16 then another 3/16-3/8. I like Tenex ends, but you can also do a dyneema
to sta-set end for end pretty easily.
Alternatively just start with 3/16 dyneema and go strait to the 3/8 sta-set tail. A little more costly (not much really), but fewer steps.
Dyneema - end for end splice - http://www.samsonrope.com/Documents/...or_End_WEB.pdf
Dyneema/double braid end for end - Splicing Amsteel to Sta-Set