Bypassing Heat Exchanger

I've not seen this specifically discussed here, but how does one bypass the heat exchanger? I'm having overheating issues and I've replaced pretty much everything else in the cooling system, and bypassed the heater core and it is still overheating. Bypassing the heat exchanger is my last idea, but I'm not exactly sure how to do this.

Do I bypass it at the aluminum pipes underneath of the hood, or should I bypass it closer to the heat exchanger itself, underneath the car? If anyone has a PDF of the coolant system that would be nice so I can get a good idea of where the coolant is going and if there is anything else it is cooling beyond this.

Edit: the irony is that once I bypassed the heater core the other day, it drove perfectly fine for about 30 minutes. Once starting up the car again, it was back to overheating. It really makes no sense to me. I really thought I fixed it. I took it to the dealership some months ago and they were essentially useless in diagnosing the problem. They just wanted to replace every part that I had just replaced, $500 a part. I wasn't about to do that.

Water pump (replaced twice)
Thermostat (replaced three times)
Radiator (replaced)
Both radiator hoses (replaced)
Coolant reservoir (replaced)
Bled air (multiple times)
Heater core (backflushed, and later bypasssed)
Checked for other leaks
Everything replaced with stock Toyota parts

 

I forgot to include that I replaced my 2012 engine with a 2017 engine, with less than 50,000 miles. The old engine blew a headgasket due to overheating. I've been (intermittently) trying to diagnose the cause of the overheating for a year now (while not driving it longer than a few miles at a time, to make sure it doesn't blow this headgasket).

There's a whole forum post devoted to attempting to diagnose the overheating (I'm ashamed to admit I inadvertently hijacked someone else's post, but they appeared to be through with it ). To avoid redundancy, I'll post the link to that:
Need help! Gas engine overheating. Cannot resolve. | Page 9 | PriusChat

MY thread, specific to my car, is here (but that was from before I swapped my engine, or even realized I needed to):
Car knocking, changed spark plugs, problem persists | PriusChat

Why am I creating a new thread, one might ask? I thought the subject of heat exchange bypass deserved it's own thread. I certainly do welcome any thoughts to the insanity. I'm at my wit's end. I've made up my mind that when I get this thing fixed I'm selling it and getting a different car.