I agree @Liz the pot. Even as a mere novice compared to most, scarifying at this time of year will spell disaster for a lot of my clients as they either physically can't water ther grrass or can't be bothered to do it if a load of seed needs spreading. The state of the lawns I've inherited are full of moss (probably 80%+) of them are and some are practically moss lawns with hardly any grass at all - they're shocking. Gonna bide the time until at least September, maybe the end of that month in case we have an 'Indian summer' and it all goes pear-shaped.
Next year try out MO Bacter on one lawn as an experiment to see what results you get. It's a pet friendly fertiliser that is slow release and will eat away the moss rather than turning it black and this year I'm very happy with its performance. The lawn which I tried it on is used by dogs, had moss in patches so I simply scarified it in the spring and applied the fert. The moss remaining simply disappeared over a matter of weeks and it's had 2 applications and has a nice thick coverage of grass. Does need to be applied on the heavy side, likes it warm and wet to start with but the instructions talk about its ability to eat thatch as well so no scarifying needed but I tend to think you need to scarify to encourage growth which you do get if you use a fixed blade scarifier that's capable of cutting in. I will have to see a core sample to see if the various thatch levels are altered so I'm not sure about that side of the product as yet. No worries about staining or scorching either as an added bonus. I don't hire scarifiers as they are almost never fixed blade machines and are free swinging setups so the blades don't cut in.