New radiator or unclog a partially clogged one?

That's great!
I hope that has resolved the issue for you.

 

To make sure the basic point is not missed ... the problem explained to you at the auto parts store (makes sense to me) is due to MIXING of two INCOMPATIBLE coolants. That is pretty much the only thing not to do. Once you've got the problem, got vinegar in there, got some flush solvent in there, etc., the main thing to do is to get it cleared out as well as you can and then pick a coolant type (almost any one you like) and stick with it.

Once the system is 95+% drained and flushed, that last 5% may be tough to clear. At that point, continuous or continual flushing with hose water is about the only way to really get close to 100% cleared out. The hose water / tap water is not ideal, but it is far better than leaving contaminants in there.

 

Just for a data point:

When doing the EGR cleaning at the outset I drained just 2 liters. This was guesstimate, I was hoping to drain enough that the coolant level would be completely below the EGR system. Turned out good, no spillage when EGR cooler hoses pulled off. There was an ounce or two trapped at lower back corner of cooler. It surprised me at first, but I only spilled maybe a tablespoon, added the rest to the previous drain.

After I was done, I poured all the drained coolant back in, with the vent valve open till coolant started out, then closed it. Spilled next to nothing. I also squeeze hoses during the fill process. When it was all poured back the level in the reservoir was at least 1/2" higher, maybe closer to an inch. After one or two days driving it settled back down to previous level (at full mark).

 

Tap water really won't harm it. It would take a LONGGGGG time to harm it.
Doesn't hurt to use just distilled water though. 2 or 3 flushes would be enough.
And you should use the Toyota coolant. That is what the car is designed to us.
Why risk using something else and screw up all the hard work and pain you've already gone through????

 

Almost everytime, you'll have to add some coolant after the engine cools.
That is why you're suppose to check it.
Just fill it to the top part of the "full" line, while on level ground. Then check it after it
cools from the next time you drive it a distance.

 

It's reassuring if it's dropped after a drive; it's working out the air pockets.