Hopefully you've got financial records which will show that you paid the deposit, you paid all the mortgage payments, you received all the rent, you declared all the rent as your own income and paid income tax on it, and your father never paid a penny towards the house or received a penny from it.
That should be enough to satisfy the revenue that your father was a bare trustee only of his share in the house; he never had a beneficial interest.
Ideally you would also have an acknowledgement from your father, dating from the time the house was purchased, that he is going on the title purely to facilitate you getting a mortgage; and that he does not intend to contribute towards the purchase of the house or to acquire any beneficial interest in it. Obviously, you don't have that but in the crazy pre-financial crash days people were slapdash about such things, and the revenue understand that. If you have everything else the Revenue ought to be satisfied.
I don't understand your solicitor's advice. On the facts as you give them this looks like a fairly clear case to me. Possibly there are some additional facts not appearing in the OP that would explain the solicitor's position but, if not, I'd be looking for a second opinion.
Do not backdate a deed of trust. That's forgery. If that's what your accountant is really suggesting, find another accountant. But there's no objection to executing a deed of trust, dated as of now, which sets out the facts about the purchase of the house and who paid for it, and in which your father declares that he has only ever held a nominal interest in the property on your behalf and has never had a beneficial interest.