Ford recommends, no additives. Marvel 'mystery' oil was for engines made 50 years ago, with sticky valves and lifters. It is more of cleaning product. New engines use Variable cam timing. They need good oil pressure to work. Use the recommend oil only and keep it full.
But the OP's 2003 is 1990 technology (designed way before that) so it is 30 year old design.
nothing in there to warrant not using a high detergent additive. They can do wonders for a tapping lifter with a speck of dirt in it or won't pump up.
Also fresh oil (op said they did oil change after it started ticking) esp with synthetic can clean up a sticking lifter.
They are superseded spec-ed to 5w-20 anyway now which is thin and should get about anywhere oil can or should get.
There are certain conditions where the 5w-20 or even 5w-30 (modular should never really be run with anything thicker than 10w-30 or 5w-40 but many have for years without clogging up or starving) on some engines can be too thin and cause the timing chain tensioner to not build pressure when it leaks out and past tensioner too quickly and a different weight of oil can stop that ticking.
Always variables specific to conditions and history. The manufacturer recommendations are very generic to cover a very broad range of climates and conditions.
An oil you could run in an engine in Florida would destroy one in Alaska....for an extreme comparison.
I ran a 1994 (but was jasper reman) in 1999-2001 4.6 on Mobil 15w-50 all year long.
temps got down to teens maybe single digits and still running well when I sold it.
I have a friend with a 95 Town Car with original engine with about 240K. It leaks and puffs valve seal smoke. He has run 15w-40 Rotella for the last 4-5 years.
I keep telling him it will eventually clog up and oil light will come on and loose pressure but it keeps running well. Stopping - not so much. Had to replace every inch of brake line od the entire car in sub 20 degree weather OUTSIDE by flashlight at times over 3 work sessions.
I'm a glutton for punishment.