list manipulation - Is there a faster way to create a matrix of indices from ragged data?

I have data that is given as a list of ordered pairs mixed with scalars. The pairs can contain infinite bounds. My goal is to convert the data into an index used in future computations.

data = {{1, ∞}, {-∞, 2}, 3, {2, 2}, {2, 3}};

This gives me all of the unique values present in data.

udata = Sort[DeleteDuplicates[Flatten@data], Less]

==> {-∞, 1, 2, 3, ∞}

Now I use Dispatch to create replacement rules based on the unique values.

dsptch = Dispatch[Thread[udata -> Range[Length[udata]]]];

Finally I replace the values with their indices and expand scalars a such that they are also pairs {a,a}. This results in a matrix of indices which is what I'm after.

Replace[data /. dsptch, a_Integer :> {a, a}, 1]

==> {{2, 5}, {1, 3}, {4, 4}, {3, 3}, {3, 4}}

NOTES:

1. 
   
   

   The number of unique values is generally small compared to the length of data but this doesn't have to be the case.

   
   


2. 
   

   Any real numbers are possible. The data I've shown simply gives a sense of the structural possibilities.

   
   

Question: Is there a way to create the final matrix of indices that is much faster than what I'm doing here?

Edit: To test the how potential solutions scale I recommend using the following data. It is fairly representative of a true-to-life case.

inf = {#, ∞} & /@ RandomChoice[Range[1000], 3*10^5];
neginf = {-∞, #} & /@ RandomChoice[Range[1000], 10^5];

int = Sort /@ RandomChoice[Range[1000], {10^5, 2}];
num = RandomChoice[Range[1000], 5*10^5];

testData = RandomSample[Join[inf, neginf, int, num]];

Answer

A modest improvement when you replace Replace[...] with Transpose@Thread:

 (udata = Sort[DeleteDuplicates[Flatten@testData], Less]; 
 dsptch = Dispatch[Thread[udata -> Range[Length[udata]]]]; 
 out1 = Replace[testData /. dsptch, a_Integer :> {a, a}, 1];) // AbsoluteTiming 
 (* {2.1282128, Null} *)


 (udata = Sort[DeleteDuplicates[Flatten@testData], Less]; 
 dsptch = Dispatch[Thread[udata -> Range[Length[udata]]]]; 
 out2 = Transpose@Thread[testData /. dsptch];) // AbsoluteTiming 
 (* {1.9421942, Null} *)
 out1==out2
 (* True  *)