Key upload seems slow on matrix.org

This issue has been migrated from [#4395](https://github.com/matrix-org/synapse/issues/4395).

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Uploading keys as part of E2E key backup seems slow to me. Here's a capture of my recent attempt on matrix.org with PII removed:

```
2019-01-15 20:15:48,131 - synapse.access.http.8080 - 302 - INFO - PUT-34926278 - - 8080 - {@jryans:matrix.org} Processed request: 5.185sec/0.003sec (0.100sec, 0.024sec) (0.968sec/2.317sec/403) 2B 200 "PUT /_matrix/client/r0/room_keys/keys?version=16 HTTP/1.1" [0 dbevts]
2019-01-15 20:15:51,011 - synapse.access.http.8080 - 302 - INFO - PUT-34926997 - - 8080 - {@jryans:matrix.org} Processed request: 1.987sec/0.001sec (0.080sec, 0.048sec) (0.407sec/0.925sec/403) 2B 200 "PUT /_matrix/client/r0/room_keys/keys?version=16 HTTP/1.1" [0 dbevts]
2019-01-15 20:15:54,246 - synapse.access.http.8080 - 302 - INFO - PUT-34927329 - - 8080 - {@jryans:matrix.org} Processed request: 2.315sec/0.000sec (0.084sec, 0.036sec) (0.390sec/1.173sec/403) 2B 200 "PUT /_matrix/client/r0/room_keys/keys?version=16 HTTP/1.1" [0 dbevts]
2019-01-15 20:15:54,989 - synapse.access.http.8080 - 302 - INFO - PUT-34927390 - - 8080 - {@jryans:matrix.org} Processed request: 2.736sec/0.001sec (0.052sec, 0.004sec) (0.172sec/0.339sec/202) 2B 200 "PUT /_matrix/client/r0/room_keys/keys?version=16 HTTP/1.1" [0 dbevts]
2019-01-15 20:15:55,022 - synapse.access.http.8080 - 302 - INFO - PUT-34927676 - - 8080 - {@jryans:matrix.org} Processed request: 0.195sec/0.004sec (0.000sec, 0.004sec) (0.007sec/0.013sec/3) 2B 200 "PUT /_matrix/client/r0/room_keys/keys?version=16 HTTP/1.1" [0 dbevts]
```

Request body size:

* First 4 requests: ~165 KiB
* Last request: 0.9 KiB

Looking at the first request for example, we have:

* 5.185 s total processing time
* 0.968 s DB scheduling time
* 2.317 s DB txn time
* 403 DB txns