Quarter the logs,dont halve them.It sounds like you are pulling them obliquely to avoid the root plate? If so,with the gear you have,bust them into quarters,round off (snipe) the sharpe edges and get your connection point under the log as much as you can (provides lift)and towards the hillside (helps prevent rolling) and just take it from there.
You will manage and frustratingly what worked for the last bit might not work for the next bit etc,take it slowly and get well out of the way.
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