I think you still can file the police report. If you ever talk to her or her husband, try to record the conversation. The fact that they did not file the claim with the insurance company must indicate that they know it is not your fault. Remind (even if it is only bluffing) them you are willing to go to court for this and they will have hard time explaining why they did not contact the insurance company if they think you caused the accident. If you cannot record the conversation, bring 3rd person to listen to the conversation and let them offer you again the settlement deal. Then, tell them good luck trying to explaining why they offered you $750 when they claim you caused the crash.
They are thinking they can get off this easy as you have no proof. Once they know that they have now provided you new proof, they won't want to go through hassle and trouble try to dodgy extra $750.00.
You must be firm and serious and tell them that you are in the process of hiring lawyer and would like to sue them for trying to deny the accident...which is a case of hit and run...kind of. If they think you are bluffing, it won't work. But once they believe you are serious (or nuts), they will be very likely pay up. Talk to them on a speaker phone and record the conversation. It will surely reveal that they know they did it. Then remind them you have now recorded proofs that you will submit to the lawyer and police to get the report. For them to mention you have no proof (if you can get them to say that again) will indicate they are dodgy.
Another evidence for you is that she gave you her insurance detail after the accident. Why would she give you hers if you hit her? Shouldn't you give yours to her instead?
Once you get these few points obtained, explain to them firmly but politely and tell them your plan of action. Also, remind them that they tried to deny their action which should be considered criminal.
If you feel uneasy of bluffing, once you obtain the above things, you may really just hire a accident lawyer. There are many who will only charge you once you win the case. Your case will be a easy and simple win. If you explain to the lawyer, they will be able to tell you you got very good chance of winning. Once the lawyer decide to take your case and (the lawyer) send a letter to them advising them to hire a lawyer, they will contact you to ask to settle it ASAP.
Don't give up and go get your money! Cheers!