Spreading lime with a manure spreader.

I have some 10-20 foot wide strips around the outside edge of an alfalfa field where the alfalfa looked weak after germinating and then slowly died over the summer. I did a soil test on these strips and the ph came back at 5.5 and very low in calcium. I limed this field heavily for a few years to get the ph high enough before planting the alfalfa but the spreader trucks must not have been throwing the lime all the way to the edge and that's why I still have a low ph strip around almost the whole field.

The trucks spread about 50 foot wide so I If have them spread the outside edge of the field again to get over what they missed It will also we way over liming a 30 foot wide strip around the field since it's only a 20 foot or less strip that needs the lime. I have been trying to figure out how to get this limed without over liming part of the field. I got to wondering if an old NH manure spreader would spread the lime since I don't think they have a very wide spread pattern? I think I can borrow an old manure spreader if it would work. If not any other ideas of what I might could use?

Spreading lime with a manure spreader.