How are the alternative solutions presented in the satirical essay "A Modest Proposal" going to solve the Irish predicament?
The short answer is: They are not going to help the Irish predicament. "A Modest proposal," Swift's satirical essay confronting the Irish predicament, was written in 1729. In the early 1700s, Protestant King William had succeeded by the then present Catholic King James II. Irish Catholics were being punished by the Protestant government for supporting the former, lawful Catholic government (always and everywhere: religious wars and punishments...).
To illustrate, the land had been gifted to English Protestants so the Irish only owned 5 percent of their own land. Irish Catholics were required to disavow Catholicism and embrace Protestantism--a big request at a time when the only church was the Catholic Church...and the heretical protesters and dissenters, the Protestants backing Luther.
Swift, though he was not at all pleased to live in Ireland, preferring London, wrote "A Modest Proposal" as a way to shock the English, through the elegant use of wit and humor and absurdity, into turning to a moral code that embraced humanity instead of rejecting humanity. All the alternative suggestions Swift proposes through his rational and calculating essay speaker are outrageous and deplorable in the extreme.
Swift's hope was that readers would recognize the utter folly of the prevailing practices in and attitude toward Ireland and the Irish and come up with serious, and perhaps modest, proposals for solving the Irish predicament. Such solutions would need to start with religious tolerance and proceed to restoration of lands to drive off poverty.