I could be wrong here but i dont think that little play in the ball joint would cause your problem. I have had much more play than that and had no wiggles under the conditions your talking about.
Pulsing under braking is most certainly a rotor problem or potentially a wheel bearing issue. With the exception of the caster on the front end, during braking all your forces are fore/aft on the truck. If your ball joints had play and you nailed the brake, yes they might shift but they wont shift back and forth causing a vibration. If your toe in/out is off it will put extra bind on your ball joints causing them to wear faster(like mine). usually you will hear them click when you come to a complete stop or when you turn the wheel while sitting still or moving slightly. I would definitely investigate a little more before settling on the ball joints. It could be the joints in your steering/drag link setup. could be unbalanced tires. It could be shot axle pivot bushing that shift around during high speed cornering.
When doing your ball joints yes you do need to remove the caliper, rotor/hub assembly and slide the axle out after you unbolt the bearing race/spindle. If youve done that before and have all the tools your more then half way there. With the axle out you can gain access to the inner castle nut. once both are loose you take a big hammer and whack it till your assembly is loose. from there its just a matter of having/using the ball joint tool.
The nice thing about a job like this is you can do one side and gauge the time it takes to do. If you cant get both done do the other side the following weekend.
as far as price for parts, the local parts store sells the ball joints for $15-$35(moog). So $100 for ball joints. Even if you replace the rotors as well and bearings i cant see it being more than $250 in parts. If a shop tried to charge me $1200 i would throw a fit. But then again I only take my vehicles in for inspection.
There is enough help.knowledge here to walk you through it if you decide to give it a shot.
oh and make sure the new joints you get have greese fittins with them, and make sure the upper grease fitting is a 45degree angle or you'll never get to it.