Seeking advice for my 5 year old in Lidcombe

Seeking advice for my 5 year old in Lidcombe I have a 5 year old with a stutter and we're currently going through the Lidcombe program but I'm uncertain if I should continue or not. ​ My father and sister both have a stutter, and I have problems with it in a very minor way, so I feel like this has got a heavy genetic influence. He's always had a speech delay and was behind in developmental milestones for different sounds (ie. his "f" sound, "s" sound, etc). We had him in therapy to work on improving his sounds because understanding him was very difficult. He's better now in that regard, but has a stutter which started around age 4. ​ We started Lidcombe around then with a speech therapist, and his scores seemed to improve after doing the program for about 4 months. Then I lost my job and we couldn't afford to continue. His stutter got worse over the next 3 or so months and after I got another job I started him up on Lidcombe again. It's been about 2 months back on the program, only doing sessions every second week. We've kind of been in a rut with it and I'm not sure if it's really helping. I also don't like how the program almost punishes him for stuttering by having him repeat things. It's been hard for me to focus on it as I'm very busy at work and generally I find the program challenging to keep up with. ​ I've been reading that Lidcombe is only really helpful before the age of 6, so he doesn't really have much time left (he's around 5 and a half) so I'm wondering if it's worth continuing or not. (I'm also unsure if "6" is definitive for all this) ​ One question that bothers me is if your father was in this position, would you want him to do all that he could to improve your stutter? It's been tough for me but I want to do what's best for him, so if that means sticking with it for a bit longer then I'll do that. ​ Just wanted some input, and perhaps some recommendations on other programs that can be helpful after the age of 6. Much appreciated!