Fortifying re-projected shapefile for ggplot2 in R

I have a shapefile of US county boundaries which I got from the NHGIS. I can load the file using the rgdal package and see information about it:

library(rgdal)
shp_1860 <- readOGR("shp", "US_county_1860", stringsAsFactors = F)
summary(shp_1860)

# Output:
Object of class SpatialPolygonsDataFrame
Coordinates:
       min     max
x -2356112 2258225
y -1337373 1565782
Is projected: TRUE 
proj4string :
[+proj=aea +lat_1=29.5 +lat_2=45.5 +lat_0=37.5 +lon_0=-96 +x_0=0 +y_0=0
+datum=NAD83 +units=m +no_defs +ellps=GRS80 +towgs84=0,0,0]

You’ll notice that the projection is a little unusual. But what I really don’t understand is the latitude and longitude: what do those values mean? Why aren’t they latitudes and longitudes in the vicinity of the United States?

I can fortify this shapefile for use in ggplot2, and plot it without a problem.

library(ggplot2)
shp_1860_df <- fortify(shp_1860, region="GISJOIN")
p <- ggplot() +
  geom_map(map = shp_1860_df, data= shp_1860_df,
           color = "black", fill = "white", size = 0.1,
           aes(map_id = id)) +
  expand_limits(x = shp_1860_df$long, y = shp_1860_df$lat) +
  coord_equal()
print(p)

I get a map just fine with that code. If I replaced coord_equal() with the more logical coord_map(), R and my computer always crashes because memory use skyrockets. I presume this is because of the weird coordinates.

I thought I would re-project the shapefile in order to plot it.

shp_1860_proj <- spTransform(shp_1860, CRS("+proj=longlat +datum=WGS84"))
summary(shp_1860_proj)

# Output
Object of class SpatialPolygonsDataFrame
Coordinates:
        min       max
x -124.7625 -66.94993
y   24.5211  49.38436
Is projected: FALSE 
proj4string :
[+proj=longlat +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0]

Notice that the latitude and longitude now have values that make sense. I can plot this new shapefile using base R without a problem, e.g., plot(shp_1860_proj). But when I try to fortify it, I get an error:

shp_1860_proj_df <- fortify(shp_1860_proj, region="GISJOIN")
Loading required package: rgeos
rgeos version: 0.3-1, (SVN revision 413M)
 GEOS runtime version: 3.3.3-CAPI-1.7.4 
 Polygon checking: TRUE 

Error in createPolygonsComment(p) : 
  rgeos_PolyCreateComment: orphaned hole, cannot find containing polygon for hole at index 6

What is the right way to go about re-projecting and then fortifying this shapefile? Alternatively, can I re-project it after I’ve fortified it?