The Ki-84 isn't a monster... Very capable, but no monster. The 109F-4 or 109G-2 are very much its equal, and both of these date back 3 and 2 years (respectively) before the Ki-84 saw combat. Likewise, the 1943 vintage La-5FN can, and will give the Ki-84 all it can handle. Any of the Corsairs are a real threat to the Ki-84, with the F4U-4 dominating it without drama (then again, the F4U-4 is the best air to air fighter in the plane set). Those early 109s are not very lethal in snapshot opportunities, so you really have to maneuver for a kill. But, that's the fun part. Except that you're more vulnerable to the pickers...
Last evening, I ran across a P-47D-25 flown by FastRide (whoever that is...). We merged at about 2k, and I reversed hard for the kill. It took about 10 seconds to get on the Jug's six. So, FastRide pulls off power and dumps flaps. He begins weaving. I took a snapshot (scoring well enough), then went vertical and rolled back in. A few more hits. The Jug is still flopping around, helpless, when I see another Jug diving in, just 1k out. I break right, nose low and haul around. The Jug can't get guns on and blows by. I spot the other P-47 turning and he's at my 10 o'clock, level with me. We are on a heading to intersect, and just before we do, I go vertical. The FastRide pulls his nose up and sprays. 1 ping on my 109, but it gets my oil, although it's inconsequential.. I drop in on his six again, and once more FastRide dumps flaps and does his best to force an overshoot. To no avail. I just work up and down, and a 20mm hits his cockpit just as a picker makes a run (I tend to dislike picking, from both friend and foe). I went after the other Jug, but someone ran him down first. I had to settle for just the one as I was running out of oil.
Anyway, the facts are that the P-47 can survive these fights, but it depends on how poor the enemy is, rather than how good the Jug is. Down in the weeds, without much E, it's just target practice. You have to fly the P-47s to their strengths, and only resort to maneuvering with flaps in desperation. Come in with some altitude, know where the enemy is, and never, ever waste E for low percentage shots. Keep the Jug light and if you have to skedaddle, do so wisely.
Go back about 8 years, and one of the most fearsome squads in the game was the 56th FG. Lots of capable pilots, who flew well as a team and exploited the P-47's strengths. Their discipline and wingman tactics made it very hard to isolate and beat them one at a time. You would quickly find yourself very busy.