Lots of "non-qm" loans out there that will add up deposits into a personal or business bank account over 12-24 months. Fastest growing segment of the market. Some are doing the 50% thing as you indicated, some subtract withdrawals, some use a CPA letter (that CPAs don't like to write, most will outright refuse).
Currently, market-wide, fewer than 50% of preapproved buyers using one of these loan programs actually make it to the closing table. The fastest growing segment of the market also has the lowest customer/consumer/client satisfaction rate.... Did I mention they have trash loan terms/conditions/rates too? In all honesty, the total value proposition between the operational incompetence and the trash terms/conditions/rates is such that HML is a better overall value even if the rate is higher. If you want to "get in the door" with HML, then refinance into non-qm, that's not crazy.
Maybe someday someone will solve non-qm. But that day is not today. Non-qm is just throwing spaghetti at the wall, and hoping something sticks -- otherwise you lose your earnest money deposit (the LO loses nothing, so why not promise the world?).
You aren't going to like it, but the answer is to get honest with Uncle Sam when you do your taxes, that way you can get some of his wife's (Aunt Fannie Mae) super cheap subsidized money in a conventional conforming loan, rather than non-qm.
