I started out with graphite 30 yrs ago. 4-5-6 wts. And coincidentally, mostly on the Little J. A case could be made that the graphite back then was slower than the rods being made today, but honestly, there are so many options anymore, especially from custom/smaller makers, in many cases that won't necessarily break the bank, that you can basically get whatever you want.
Absolutely cast a pile of rods to see what you like. That is the best advice given. Traditionally, rods for wet fly swinging/streamers were slower flexing than dry fly actions, but sometimes that didn't/doesn't mean anything depending on what you liked in terms of feel, and how you integrate a given rod with your casting stroke/preferred style.
About 15 years ago a buddy insisted on lending me his 7' split bamboo rod 5 wt for a couple weeks. It was a real fancy-pants rod, it would have set me back a weeks salary or more; I was almost too afraid to use it. It was like agreeing on going to the dance with your buddies out of town cousin, and on sight, seeing she was some way out of my league goddess.
After I got the balls to try that cane rod, it was a revelation. It was the sweetest casting rod I had ever used. It opened a new perspective on fly rods for me. No way I could afford that one, I learned about how generally, bamboo and fiberglass can have similar feel, and found that to be the case for me. Since then, I have gotten rid of all but two graphite rods and pretty much exclusively fish bamboo and glass for trout.
My specific recommendation for you will be biased towards vintage bamboo-just offered up as a 'third way' option, in what I would consider 'if I only had one rod to fish the Little J'; and yes, while I live in Iowa, I spend close to a month in PA through the year visiting family and have fished the Little J many, many times.
8-1/2' South Bend 346 HEH (casts a modern 5 wt)
8-1/2' Heddon 2F #10 (and higher grades) (casts a modern 6wt)