I am not sure what you mean by splitting the original position. If you bought it this year, you can go and re-enter the buy into 2 lots. Then on the date of the transfer you can either sell one lot ("no tax effect") and buy back to new broker, or you just change the name and do a genl jnl memo detailing what you did.You can sell the original position for "no tax effect" and buy back 2 lots (one for each broker), or
You can sell one lot as a partial sale from the original position (broker A) for "no tax effect" and buy back that lot (broker B) with same cost info but with a new qualifier for the correct broker (or however you designate that).
If you do this, I would suggest a memo on both transactions to indicate what is being done (i.e. transfer 100 share lot from Broker A to Broker B)