My homeschooled son applied to colleges in several different states. All of them wanted confirmation that he had completed a high school program according to our state’s regulations. That actually protects us because other states can’t impose extra requirements retroactively.
The difficulty for OP is that states that require paperwork to homeschool (NYS requires a letter of intent in Sept, a curriculum list, a yearly plan of instruction, quarterly report cards, year end reports, and yearly test results) are not going to provide the proof of high school equivalency without it. And colleges are going to demand all of that and more (counselor letter, outside teacher recommendation(s), & school profile), so you really can’t fake it.
OP could encourage her son to take the GED and enroll in the local community college, but then he loses out on any merit aid he may have gotten if they found a way to pay the high school. If it takes them a couple/few years to pay it off, would he be considered a nontraditional student who wouldn’t qualify for merit aid, or doesn’t that matter? Unless they can work out a payment plan or he can get merit aid later, I’d take the GED, start at cc, and work on getting that debt cleared. On the plus side, if he has a cc degree, he no longer needs his high school record when he applies to a 4-year-school, so they may be able to stretch the payment plan out a little.