Lots of good advice here so far, and you are doing a lot of things right already. Here are a few more suggestions.
Puppies don't want to soil "their space". When you confine them (in a crate or similarly small area), they will probably not mess there. This gives you the perfect opportunity to use this as a training aid. Confine them when they are alone and/or resting; when you get home or when they awake, immediately take them outside to do their business. When you're home anyway, and they're loose around the house, take them out as frequently as you can - every 2-3 hours, or any time they wake up from a nap, while they're still housetraining.
I can't say enough about the benefits of crate training. Dogs see it as their own "den", their own space. We have used crates to help train all our dogs and they have worked like a charm. When we go to bed or leave the house, the puppy goes in the crate, with the door locked. When we wake up or get home, we take the puppy outside to do his business. They have all been nearly perfectly housetrained within a week or two.
Once they're fully trained, we still leave the crates set up with the doors open, and they often sleep in there. We rarely lock
Cosmo, our adult bearded collie, in his crate now; he has the run of the house, even when he's home alone, and he's fine.
Layla, our nine-month-old puppy who is his daughter, is still pretty young; she has the run of the house even at night, but we still lock her in the crate when they're home alone. Some time soon we might let her have the run of the house when we're away, as well. But we'll still leave the crates set up; it's their "den", their "home", and their own special place, where they can rest any time they want, without being bothered.
You'll find excellent tips and information about crate training and housebreaking on the website for
Midwest Homes for Pets, a leading manufacturer of pet crates. Granted, they have a financial interest in crate usage. But let me tell you, it works!
There are lots of different kinds of crates these days. There are collapsible metal crates. There are also collapsible fabric crates that are very light weight. We keep one of each for each dog.
Shop around on price. And check the internet. You may find that your favorite store chain shows lower prices on their website than in person, but they will often meet their own web prices (if not those of others) if you bring a printout of their website to the store.
I don't think much of "potty pads". IMO they train the dog that it's okay to do their business indoors, but in certain places. I guess that's fine if you have an area (basement?) that you want to use for that purpose... but if you want them to only go outdoors, then I think you're better off training them that way. Just my O.
I have heard that you can expect puppies to hold themselves for two plus their age in months, in hours. So a four month old puppy can hold it for six hours. With our latest puppy, Layla, that worked up to the age of four months. She was then on a six-hour limit for 2-3 months after that. Now, at nine months, she can go the whole night (although regardless of when she went to bed, she wants to go out as soon as it gets light out).
Here's a recent photo of Layla:
and one of her next to her daddy, Cosmo:
He just went again! 
He's doing pretty well with tinkling. I really haven't had that many accidents with him. Maybe 5 or so since we brought him home and I started training him. 
