Welcome to the site!
However, this is one question that might stump all of us. I did a few searches and only came up with complete rods.
It's difficult, from what I found, to make a specialty rod like a ten foot three-four weight rod for a good price. It looks like SAGE and G Loomis are the only ones that carry blanks for this, and unfortunately they come at a price.
You might want to consider, and I know it's more pricey than you were hoping, the Greys Streamflex 10 foot 4 weight. One benefit is that you don't have to take the time to put it together. An other clear benefit is that you can send it back if it breaks and get a new one. If you break a rod that you build, you only get a blank in return for your brokenrod. This leaves you to go purchase all of the components again. I know that they don't cost much, but the time to get them and rebuild the rod is costly.
I wish that I could recommend a rod blank that would work for that price. You might have posed the toughest question yet!