A lot of lime to spread with one of them. Don't know if you could buy one that holds much more than 1K pounds. And that might be pushing it. Sure take a while.
/ Spreading Lime with belt trailers and railroad iron
With as much lime as the OP wants to spread, they will be very long time using a 3-point PTO spreader to spread it.
As for the question of having the truck's tailgate the lime on to the field and then spreading it, I think in order to get that spread evenly it will need to be mechanically spread, not just with a fixed bar. Something like perhaps a hay tedder would work, but it would be far simpler to use a towed spreader or have somebody bring in a spreader truck and use that.
If you try to tailgate it in and then spread it out, any low spots in the field will get extra lime and the high spots will get less. If you use a spreader, the whole field will get an even coat.
Aaron Z
/ Spreading Lime with belt trailers and railroad iron