A spring is nothing more than groundwater finding a way up to the surface of the ground and flowing away. Putting a well in the immediate area of a spring, which you say this is, means the water could be contaminated 'upstream' of the spring for some distance because of the water on the surface of the ground, at the spring. And moreso as you pump water out of the well because the spring water (on the ground) is going to be in the well head protection area of the well. That means the spring/surface water is in the cone of depression of the well, and your geology is sand that has no resistance to water flow from the surface down thru the sand and into the well.
And since you have a backhoe, it could be much easier to dig and build a spring pit than put in a 4" casing without a drilling rig, if that you can do that by hand.
Unless Sammy or some other driller here has used a PM to tell you how to put your 4" well in this area, I don't they will tell you how or that they think you should, or that you'll get potable water, but we'll see.
BTW, I'm from PA and outside the cities, many people are just as independent as Texans and history shows they have been since before there was a Texas. I've also been a Texan for awhile, (spent some time in Livingston and Uncertain) until last July and I'm all for self reliance and independence from government intrusion and regulations. At heart I'm still a Texan and so is my wife; except in the summer. So I'm all for what you want to do. If you do this well and the law makes you dismantle it, you would have been better off with a spring house; I don't think that is illegal anywhere (outside of cities). I'm sorry if you think my posts were unhelpful, they weren't meant to be anything but helpful, including this one.
I just remembered this... nstead of washing the casing in, you need to make a 'sand sucker' that fits inside the 4". And yes, you need screening, and maybe a gravel pack outside the screening. Here's a place all about what you want to do, I used to post there a few years ago.
http://www.voy.com/102731/