Dang, that's steep!

I'm used to hearing about a $100-200 range. I suppose it's because you have an Active, and not the regular S6. Good luck!
I've had a similar hairline crack in my screen which required an lcd panel replacement through Samsung. I was quoted at $237.00 for a replacement. Although their site clearly states that it is $199.00 for out of warranty/damaged lcd repair for the S6, I only payed $70 for the replacement. Here's what I did:
1.Take photos of the device, find your receipt, and make notes of what happened when your device stopped working (In other words, get your ducks in a row before you call for support.)
2. Follow their repair instructions for mailing in the device. Keep track of the package and when it is delivered to the repair center. In my case, they take several days to actually check the device in after receiving it.
3. You'll get a call back when they've looked at the device and made their assessment. They'll demand payment within a business day or two or they will mail it back to you unrepaired. (The voicemail i received didn't go into the details of their assessment and almost seemed threatening. "If you don't pay up, we're not going to fix this and we'll send it back to you broken.")
4. Here's where I made my case. I purchased this device based on its advertised features of being rugged and waterproof and capable of keeping up with someone who has an active lifestyle. As my pictures indicate, I did not abuse the device or do anything outside of normal operation to compromise its ability to function. I really didn't understand how a minor drop could render the device inoperable especially if there are little to no signs of damage.
I made my case to Level I and Level II support, and eventually spoke to a manager at the repair center who adjusted the final bill to $70. Be persistent, ask for an explanation and push for a reasonable resolution. Sure, the device would not have stopped working if you didn't drop it, but is it not reasonable to expect this type of device to survive drops?
I reluctantly paid, but $70 is better than $237. And I'm not sharing this to encourage you to "get over" on Samsung. It really is about demanding them to stand by their advertised product and treat it appropriately. No, they didn't advertise the s6 active as drop-proof, however, they market it as being a rugged device that meets IP68 standards (some military battery of tests regarding waterproofing and dust proofing). This would lead the consumer to believe that the device is significantly more durable than a device with glass backing.