For class J fuses up to 60 amp you can use a fingersafe tilit-out type fuseholder with a blown fuse indicating light instead of the little indicator window. The Shawmut US3J/US6J series is the best, Bussmann also makes a similar product that isn't as nice as the Shawmut.
As long as the NEC overcurrent protection rules allow it, there is no technical reason that a class J time delay fuse cannot be used when a class J fast acting fuse is called out. Class J time delay fuses are designed to withstand 500% of rated current for 10 seconds without blowing. They are dual element type, which also means they cost somewhat more than a single element fast acting class J fuse.
I use a lot of class J fuses for switchgear control circuits, medium voltage motor starter control circuits, and UPS power branch circuits - none of these uses require me to go above 60A, which is why I standardized on the Shawmut fingersafe holders with LED blown fuse indicating lamps.