I went through this with my son. I honestly don't think you can "train" kids. Really. Some of them are ready at 3, some aren't. It's very helpful to look at all that he CAN do, and not fix all your hopes and dreams on one milestone. Kids walk at different ages, talk at different ages, develop gross and fine motor skills in a different order from other kids. But the potty readiness ties us up in knots because it's just so visible - we're still buying diapers when our friends are not, the other kids are focused on "big boy underwear", and we set up this battle of wills between parent and child. And, as you say, there's the preschool thing.
So let me ask you - what terrible awful harm will come to him, long term, if he doesn't start preschool in September? Honestly, there's nothing you can do! Let it go (no pun intended). Do other things. Go to the children's museum, the zoo, the nature area, the library story hour. Join or start a play group through friends or the Newcomers Club (especially if you relocate).
You are cleaning up messy underwear. He knows what you want and expect, but he cannot do it. He's not there developmentally. Put him back in diapers, put away the underwear, and just stop talking about it. Let him know that you'll be ready when he is, but that it's not his time. You can put him on the potty and "get lucky" sometimes, but that doesn't mean his body and brain connected enough for him to know how to do this, how to anticipate.
My son was 4 before he was reliably dry during the day, and he took an extremely long time at night. But he was so awesome at other things, I really missed many of them because all I could see was the potty thing. It was a huge battle of wills, but when I realized it wasn't his WILL but his BODY that wasn't working on my schedule. When I focused on his schedule and noticed what a terrific builder he was and what a great athlete he was, it was better for both of us. So my little wet-bottomed boy DID learn to use the potty in his own time, and his Lego building skills led him to be a civil engineer, and his athleticism led him to be a track star. He took an extra year of preschool, started kindergarten at 6 instead of 5, and we never looked back. And guess what? He wasn't the only one! There were 8 boys on our street, only 2 of them were eligible to start kindergarten that year, and so all 8 started the next year, together.
You can't control his development. This is nothing he can learn, like his name and address. He has to grow into it. All you can control is your own panic. It will be better for both of you if you can do it.
Good luck!