Using the right database for massive Geospatial Queries (ElasticSearch)

Currently, we have have ElasticSearch instance with around 100m+ records that contain a lat/lng, created_at, item_id and user_id. We would like to answer these questions:

1) How many item_id are in a nearby X,Y with a radius of Z in the last T days?

2) How many unique users are a nearby X,Y with a radius of Z in the last T days?

3) How many total items, and unique users are a nearby X,Y with a radius of Z in the last T days, group by month?

We've tried MongoDB, MySQL and now ElasicSearch and we're getting no where in terms of performance (constantly under 5s). Is the only solution to move to a data-ware house model here like Redshift? Anyone have any recommendations?

Below is the search query to get

GET items/item/_search
{
   "query": {
      "filtered": {
         "filter": {
            "bool": {
               "must": [
                  {
                     "geo_distance": {
                        "distance": "10mi",
                        "loc": {
                           "lat": 40.712784,
                           "lon": -74.005941
                        }
                     }
                  },
                  {
                     "range": {
                        "cat": {
                           "gte": "now-1d/d",
                           "lte": "now/d"
                        }
                     }
                  }
               ]
            }
         }
      }
   },
   "aggs": {
      "distinct_users": {
         "cardinality": {
            "field": "uid.hash"
         }
      },
      "distinct_checkins": {
         "cardinality": {
            "field": "iid.hash"
         }
      }
   },
   "size": 1
}