Are there any alternatives to the NIntegrate method attempted here? The following numerical integration appears to gets stuck indefinitely (>> 12 hours) on a 32GB machine with Mathematica 11.2, with different (very low or high) values of MaxRecursions etc. The integral is not divergent. Tried other methods like DuffyCoordinates and LevinRule.

p1v = Table[p1[i], {i, 3}]; 
p3v = Table[p3[i], {i, 3}]; 
p4v = Table[p4[i], {i, 3}]; 
p5v = Table[p5[i], {i, 3}]; 
rv = {1, 1, 1}; 

$Assumptions = Element[p1v | p3v | p4v | p5v, Reals]
intvariables = Flatten[Join[{p1v}, {p3v}, {p4v}, {p5v}]]
intvariables1 = ({#1, -Infinity, Infinity} & ) /@ intvariables


jj1=((13/2)*(p1[3]*((-p3[2])*p4[1] + p3[1]*p4[2]) + 
      p1[2]*(p3[3]*p4[1] - p3[1]*p4[3]) + p1[1]*((-p3[3])*p4[2] + p3[2]*p4[3])) - 
    3000.*(((-p3[3])*p4[2] + p3[2]*p4[3])*p5[1] + (p3[3]*p4[1] - p3[1]*p4[3])*
       p5[2] + p1[3]*(p3[2]*p5[1] - p3[1]*p5[2]) + 
      p1[3]*(p4[2]*p5[1] - p4[1]*p5[2]) + ((-p3[2])*p4[1] + p3[1]*p4[2])*p5[3] + 
      p1[2]*((-p3[3])*p5[1] + p3[1]*p5[3]) + p1[1]*(p3[3]*p5[2] - p3[2]*p5[3]) + 
      p1[2]*((-p4[3])*p5[1] + p4[1]*p5[3]) + p1[1]*(p4[3]*p5[2] - p4[2]*p5[3])))/
   E^(I*(p1[1] + p1[2] + p1[3]))/((1 + p3[1]^2 + p3[2]^2 + p3[3]^2)^2*
   ((-p1[1] + p3[1])^2 + (-p1[2] + p3[2])^2 + (-p1[3] + p3[3])^2)*
   (1 + p4[1]^2 + p4[2]^2 + p4[3]^2)^2*((p1[1] + p4[1])^2 + (p1[2] + p4[2])^2 + 
    (p1[3] + p4[3])^2)*(1 + p5[1]^2 + p5[2]^2 + p5[3]^2)^4)


Block[{p1v = 0, p3v = 0, p4v = 0, p5v = 0}, 
   NIntegrate[jj1, Evaluate[Sequence @@ intvariables1], 
     Exclusions -> {{p3v == p1v}, {p4v == -p1v}}, 
  Method -> "GaussKronrodRule", 
     MaxRecursion -> 5, WorkingPrecision -> 10, PrecisionGoal -> 6]]