Paycheck parking is easier to describe when one paycheck goes into one line of credit. Plenty of households don't run that way. Separate checking accounts, separate cards, a shared bill account in the middle, and both people like it like that. You can still run this. You just have to decide who's doing what before the first deposit lands.
Setup one, both paychecks in. Both direct deposits route to the line of credit. Once or twice a month you draw money back out into a shared checking account that pays the bills. Personal spending comes out of separate accounts you each fund with a fixed transfer. This version saves the most interest, because your full income is sitting against the balance all month long. It also needs both names on the line of credit, and it asks the most trust of both of you.
Setup two, one paycheck in. The higher or steadier income routes to the line of credit. The other paycheck keeps doing what it always did, covering a list of expenses you agree on, out of a separate account. You give up some of the interest savings and you keep most of the simplicity. For a lot of couples this is the version that actually gets done, and a plan you run beats a better one you don't.
Setup three, proportional. Each person sends a set percentage of their pay to the line of credit and keeps the rest. That's fair when the two incomes are far apart, and it takes the argument about who's contributing off the table. The trade-off is that a fixed percentage doesn't react to a month with a big surplus, so you have to look more often to catch the extra.
Here's the thing. The same failure shows up in all three. One person runs it and the other has no idea what's going on. Six months in, the person who isn't logged in gets nervous and asks to stop, usually at the worst possible moment. Fix that with structure instead of a promise to communicate better. Both people get login credentials, or read-only access at the very least. Put the balance somewhere you both see it once a month. Ten minutes together looking at the same screen is the review described in the ten-minute monthly review that keeps Dynamic Banking on track.
Whose name goes on the account is a separate decision with real consequences, and it's covered in whose name goes on the line of credit. The short version for a two-account household: if only one spouse is on it, the other one can't move money in an emergency, can't call and get information, and doesn't automatically get the right to manage it. Make sure you've talked through what happens if the account holder spends three weeks in a hospital bed.
Last piece, and this one breaks the math rather than the marriage. Separate accounts make your total spending harder to see. So the surplus you calculated at the start can stop being real without either of you noticing. Sit down every quarter with both accounts on the table and run it again. Find your real monthly surplus walks through the number. Do it twice a year even after you're up and going.