3 way dimmer in 4 way circuit
3/4 way switch systems have a 3-way on each end and 4-ways in the middle.  As long as the smart switch is on a end (a 3-way position), it cannot possibly know there are 4-ways involved. So a simple mechanical 4-way inline is not a factor and can be disregarded.   

When using dimmers, motion sensors, lighted switch, or any sort of powered switch, those absolutely do not support LEDs ... unless they do.  And when they do, there are conditions and rules.   So when chasing this kind of problem, it's best to divide and conquer: go  back to incandescents until the problem is sorted out, then handle the "making LEDs work here" problem.