The "long term" goal of the boycott is to force the hand of government to just eat the cost of education and do away with the student loan system.
Until something snaps, Congress won't fix anything.
If the debtors take a collective action approach and just boycott their payments, it would force Congress' hand.
Instead of bailing out banks. Wipe away that debt, bailing out college graduates, who in turn can use their money as they see fit.
The boycott itself is just a temporary measure to 1) alleviate the effects of paying student loans on household budgets during a recession, 2) bog down the collections-system in the courts to shield the majority of people form collection actions, and 3) show the policymakers/businessmen that it is in their best interests and the best interests of the economy long term to fix the student loan disaster since an injection of all that money into the economy during a recession would have tangible benefits without any action on the government's part other than not collecting on those federally backed student loans.
Any penny spent in the USA is going to eventually work its way into the bank accounts of major corporations. By relying in a "trickle-up" bail-out system, each person can spend their money as they see fit.
While I think your long-term goals are good as a policy goal. I'm thinking more short/medium term because recessions are short/medium-term events. And since millenials/gen Z are so connected, and intimately tied to their student debts, the political pressure of a mass boycott would likely make your long-term goals possible while still being easier to achieve int he short term.