Due to the OP requirements philippines would start with 7m in 1900 or 20m in 1945 population. Philippine land area otl is roughly Arizonas size. This means iphilippines will be the 6 or 7 th us state in land area. So, I don't know how you define it being too big for a state.
Alaska was about 200,000 when it became a state in 1959, and I'm not sure if it's broken a million today even. From a land area, it's larger than many countries
Some parts of both North and South Dakota have recently had population densities below "Frontier level" of less than 6 persons per square mile. Some of that has recently changed with the oil boom.
IF the Philippines were to come on as a state(s), it
might be to their advantage politically to divide it up somewhat: Two Senators per state, and the House Representation is apportioned by population. Maybe Luzon forms the core of one state, the Visayas another, and Mindanao a third group. Something along those lines.