You have not mentioned any other details of the offer so I am assuming here, but you could offer to increase the deposit (and perhaps release it immediately) and shorten the settlement. When you said you were prepared to go unconditional, I assume that means that your offer is not subject to finance or any other terms so perhaps a reminder to the agent that if they wait for someone else’s offer, it will most likely be subject to finance and therefore a bank valuation which is always risky with a property requiring so much work. Best of luck!