If she refuses to disclose her financial circumstances then you have the right to insist that she does not apply for decree absolute until such time as the financial issues between you are formally and finally resolved. Since she issued the divorce petition she presumably wants a divorce so this gives you some leverage.
You do not say whether this completion of Form E is voluntary or not. I suspect that it is. If that is so then you can ultimately compel her to complete a Form E if you make an application to the court to settle the financial issues between you and the court orders that she completes a Form E. One way or another court orders can usually be enforced because courts do not make orders that cannot be enforced.
Your solicitor is absolutely right about paying her any sort of lump sum. Without knowing what her financial situation is you cannot possibly make an informed decision about that and it may indeed be a very bad move.