Record the times and duration for future use should you need to go council route.
Despite what mumsnet will tell you, they absolutely are interested in constantly barking dogs that stop people enjoying the use of their home.
My stance would always be to try talk to the folk first, but let's be honest if they're telling the dog 'did that mean lady tell you stop barking' kind of thing then they don't give a shit about you.
And from experience, in real life and the mumsnet standard, barely anyone gives a fuck about their impact on anyone until the council get involved and make it official.
I write this as someone who has a neighbour whos dog screams and howls whenever she leaves the flat (yes even at 1am, and it can be heard at the opposite side of our flat, no escaping it), and a big fuck off dog on the road that the owners put outside for it to constantly bark for hours on end, in full company of the owners whilst they're pottering about their garden .
Occasionally they get the hint by the neighbours windows slamming shut and squawk at it to shut up. It doesn't.
The other weirdo just stands by and lets the rat of a thing also bark constantly when she is home. I would have reported at least one of the fuckers but I'm moving anyway. The stupid dog owners, and person next to us who likes to light fires at 4pm, blast radio so loud you can't hear your own voice when outside, and shouts for normal conversation (and you can hear them when you're inside clear as day, word for word) and spends the summer revving motorbikes for hours in the garden, are the absolute reason. Latter person knows they're a pain in the arse, spoils everyones enjoyment of their garden too because there is not a sunny day they aren't doing this, and has clearly told people they don't give a fuck and has threatened people for complaining to them they're noisy.
And yes I'm a dog owner. And no, it doesn't bark. Yes I have camera/audio for when I'm out of the house to check dog is settled and not fretting. It's not hard to train to be honest.
So, I'm going to be very unmumsnetty and say don't bother even trying. Your idea of suggesting a way for their dogs to get used to you is a brilliant and polite way of going about it, and perhaps is a worth a shot. But otherwise I'd just go heavy handed.
People like this fuck me the hell off. And you can bet they're mumsnetters too. No way is anybody this unaware of what an annoying selfish person they are.