No, no, no way sign over your property without receiving all the money. I note that he was your partner not your husband, which makes your position even more difficult.
If you did agree to sign over the property:
You can put a caution on the property which would notify any potential purchaser that there was a dispute. This would stop him selling but would not give you the right to force him to pay up.
You could put a charge on the property
BUT
It would need his permission and the mortgagors permission. Assuming they agreed the mortgagors would have priority and there debt would be paid off first. Your rights would be limited - you could not force him to sell the property, so if he stayed put then you would not have anyway to force him to pay up.
I assume you are presently Joint Tenants, this means that you do have the right to force him to sell the property to access your equity. This is your bargaining position AND YOU MUST NOT GIVE IT UP.
Explain calmly that you have taken legal advice and your solicitor has advised that your name on the deeds is your only security. The fact that he has paid some of the equity first does not weaken his position as there is no way that you could collect for the same money twice - ie: if he sold the property then the payment that he has already made would be deducted from the balance of the equity.
Judge Flounce disclaimer
I am a qualified solicitor specialised in commercial property though presently not practising. However, registration laws have recently changed - I don't think that this would make any difference to your position however. I have to advise you to take proper legal advice.
However, your ex-p is trying it on and probably knows it so be tough.