This method is feasible on the surface, but it is difficult to realize in the current implementation process.
The demand for price-limited housing in Beijing is very tight, which leads to very strict qualification conditions in Philadelphia. You should not only look at your current income certificate, but also look at your historical income and tax records. Even if you artificially reduce your income this year, your past record can't be eliminated, which may lead you to fail to meet the application conditions.
In a big city with strict audit, unless you can use internal relations, it is difficult for you to obtain the qualification for purchasing limited-price houses through tricky methods, and shortcuts are basically impossible. If there was any shortcut, it would have been used long ago, and it had been discovered by the management department and blocked the loophole.