Send raw transaction from geth when not synced (exceeds block gas limit)

Question

I have a geth node which is not synced and I want to send eth.

> TX={ from: FROM, to: TO, value: VALUE, nonce: NONCE, gas: GAS, gasPrice: GP }
> personal.unlockAccount(...)
> SIGNED_TX=eth.signTransaction(TX)
> RAW=SIGNED_TX.raw
> eth.sendRawTransaction(RAW)
Error: exceeds block gas limit
        at web3.js:6347:37(47)
        at web3.js:5081:62(37)
        at <eval>:1:23(4)

In the past I have managed to submit RAW to an ethereum broadcast web page such as https://etherscan.io/pushTx but sometimes that works and sometimes I get an error like

Error! Unable To Broadcast Txn : {"id":"1","jsonrpc":"2.0","error":"One or more errors occurred."}

This isn't enough information for me to fix anything. I would like to do it direct from geth but since I am not synced I'm getting the block gas limit error.

How can I tell geth to submit the raw transaction to the network regardless of the block gas limit?