Lime will NOT go to waste if you add it to your plot NOW< and the sooner you add it the better, as the ideal way to make lime work is to mix LIME in with your soil, so each particle of lime touches a particle of soil, that is the ONLY way it will work!
I have 30+ yrs of making food plots in PA, in countless counties all over the state! from small like yours to up to 30 acres in size DEER/wildlife plots!(30 yrs part time farmer as well)
Lime is a never ending thing and you will need more than a 187 lbs IMO to make a dent in things, its better than nothing, but its NOT going to make much difference adding NOW< for this first planting!
if your NOT going to MIX the lime in to get it to work, it will take a LOT longer to just break down and leak into the soil, and to do that you need MORE Than the recommended amount, so it has extra to leak from top/above ground, into a few inches of soil to get to where the roots are in your plantings!
snow and rain will again, help leak/break down lime and get it into the ground, but its a very very slow going process that takes TIME and a lot of it, even mixing it in isn't a FAST fix!
1.9 tons is over kill , but I wouldn';t hesitate to add a good 500-700 lbs to this site if it was me here!
Pa has very rocky poor soils and most that are NOT, are long time now already in LARGER farms!