One detail of the plan would be a vesting period.
This is the way it works with employment security benefits. If a citizen of WA moves to TN, works for a month, then applies for unemployment benefits (AKA ESB), the state of TN may authorize the benefits but will turn to WA to reimburse the cost.
With ESB there is a vesting plan, so that the longer you stay in your new state the more it pays your ESB itself, until after a period it pays 100% of it. The citizen’s old state picks up any balance.
As I understand it, all states have this same vesting process with ESB. Employment Security is an example of a nationally-mandated social program that is wholly funded and administered by states, and the states have a mechanism for transferring money between them to make things equitable.
With leagues the same exact thing would happen. If a person moves from a Blue League state to a Red League state and draws money for social programs, the Red League state may pay the benefit out but turn to the Blue league for reimbursement, and vice versa.
However, if a league has no such reimbursement agreement, then no benefits would be paid out until full vesting occurred. Maybe a period of years.
With league SSA programs you would accrue SSA benefits in the league you happen to work in, with a few adjustments for the inevitable workplace versus home-location conundrums. A person could conceivably draw two different SSA pensions because they worked 25 years in one league and 25 in another.
But a person moving from WA to TN at age 67, with no years worked in Red League states, would receive no Red League SSA benefits. All their SSA benefits would be Blue League benefits, and vice versa.
An interesting possible effect would be this: if the leagues had SSA programs with substantially different levels of benefits, would far-sighted workers migrate from one league to the other because of higher benefits and shorter vesting time? And then, after retirement, live in the league with the lower cost of living?