Here's a Python script that will convert mongo's unfriendly date format to a string format in your exported json dump:
######################################
# About                              #
######################################
# Author:   Eric Arnol-Martin https://eamster.tk
# Purpose:  Replaces Mongo's Exported DateTime Format with Proper DateTime String Representations for Easier Import for Other Databases / Programming Languages
# Expects:  Mongo JSON Exported Pretty File.  
#           For example, a file produced by a command similar to 
#           "mongoexport -d {db_name} --host localhost:27017 -c {table_name} --jsonArray --pretty -o {table_name}.json"
# Tests:    RegEx Test Link:  https://regexr.com/68l7r
# Outputs:  Creates a copy of the input JSON file with DateTime objects replaced with their proper string representation in the same directory as the original file 
#           with the same file name suffixed with "_NEW" at the end of it.
# Sources:  https://stackoverflow.com/questions/2503413/regular-expression-to-stop-at-first-match
#           https://stackoverflow.com/questions/159118/how-do-i-match-any-character-across-multiple-lines-in-a-regular-expression
######################################
# Imports                            #
######################################
import re
from os.path import exists
import fileinput
######################################
# Actual Program                     #
######################################
path = input ("Enter path or name of file to parse: ")
prevPiece = None
content_new = ""
boolReplaceFromNextLine = False
boolHandlingLong = False
if exists(path):
    # Clear new file
    b = open(path + "_NEW", "w+")
    b.close()
    count = 0
    recordCount = 0
    for line in fileinput.input(files=path):
        count = count + 1
        if '"$date":' in line: 
            content_new = content_new[0:content_new.rindex('{')] + line.replace('"$date": {', '').replace('"$date":', '').replace('\n', '').strip();
            boolReplaceFromNextLine = True
        else:
            if boolReplaceFromNextLine:
                if '"$numberLong":' in line:
                    content_new = content_new + line.replace('"$numberLong":', '').replace('\n', '').strip();
                    boolReplaceFromNextLine = True
                    boolHandlingLong = True
                else:
                    if boolHandlingLong:
                        content_new = content_new + line.replace('}', '').strip();
                        boolReplaceFromNextLine = True
                        boolHandlingLong = False
                    else:
                        boolReplaceFromNextLine = False
                        content_new = content_new + line.replace('}', '').strip() + '\n';
            else:
                content_new = content_new + line        
        
        if line == '},\n' and content_new:
            recordCount = recordCount + 1
            b = open(path + "_NEW", "a+")
            b.write(content_new)
            b.close()   
            content_new = ""
            print('Record ' + str(recordCount) + ' processed... adding it to the file...')
            
        prevPiece = line
    
    if content_new:
        b = open(path + "_NEW", "a+")
        b.write(content_new)
        b.close()   
        content_new = ""
        recordCount = recordCount + 1
        print('Record ' + str(recordCount) + ' processed... adding it to the file...')
Adjust as needed.  This worked on a 14GB exported json file.  We needed this for a conversion from mongo to SQL Server.