Even with hundreds extra to budget for your wants, do you have enough water pressure and flow to get the job done?
A crude rule of thumb is that you need 1 PSI for every foot of throw you desired (and that's pressure at the head, not static pressure at the source). So to allow a throw of 50 feet, you need 50 PSI of WORKING pressure at the head (after all the pressure losses through pipes, valves, and backflows).
But the biggest issue, especially for a DIY job, is that general equipment available only goes upto about a 40 to 50 foot throw. However, sprinklers need what is known as head-to-head coverage. Basically, the amount of water deposited varies as the distance from the head (with most of the water going to the far end of the throw, not near as much water being deposited closer to the head). So to get even water coverage, you need to have the throw such that each sprinkler head is throwing water all the way to the next head.
In your case, to get head-to-head coverage without adding sprinklers in the middle of the yard, you need sprinkler heads that can throw 80 feet. Given the dimensions you are quoting, I don't see it happening unless there is something at the professional level (I'm just a DIY irrigation guy)... and even if there is something at the professional level, is sounds like you will have to have about 100 to 150 PSI static pressure for even the professional equipment to work.