Help! Dealer fixed inverter...then Boom! CEL, P0403 and coolant loss, etc.

Hello friends. I’ve been reading thru so many threads looking for a solution to my problems. Hoping this will look familiar to someone. I’ll try to keep it short.
I have a 2013 Prius 4- never had any problems until @ 185K, the IPM inside the inverter died and was replaced by Toyota under an extended warranty. Everything seemed ok until one week later, car has a super rough start in the morning at idle, throws CEL but smooths out and drives fine. This car has never thrown a CEL. I’m thinking that it has to be something related to the IPM replacement, so I take it back to Toyota and while they are telling me that it’s going to be $200 to diagnose, the CEL turns itself off. Instead of leaving it for diagnosing, I take it home and change plugs, pull and clean manifold, pull and clean egr valve and cooler and put everything back together, as this work had never been performed before. The throttle body was clean, no oil puddle or anything when I pulled the manifold. EGR valve was super crusty, cooler was also super crusty, manifold wasn’t too too bad, think I got small holes cleared out. Got EGR and cooler back to super shiny with pure light coming thru cooler.
Everything seemed ok for a few days, then bang- hard, misfire on cold start, CEL thrown but smooths out but then drives fine. Seems to have great power, and later CEL turns off on its own. But now I notice that coolant level has dropped since refill after egr/manifold/plug job.
A couple days later it does the same thing, this time, thinking that maybe I needed to have car recalibrate it’s idle/timing on its own, I disconnect 12v battery for an hour, which clears the CEL and car starts fine
But the next day, BANG. Same old story.
Hard start, mis-firing, rough idle is now guaranteed every start up. Coolant level continued to drop. Car has been driven about 1000 miles since EGR/plug cleaning. Car is now in garage, not being driven, waiting to be fixed.
Other than coolant level dropping, there doesn’t appear to be any sign of coolant in the engine- no “peanut butter” build up under the oil cap, oil looks nice and clean, spark plugs still look brand new, except #2 which had a little black carbon on it, but nothing that looked serious, no huge plumes of white smoke coming out of tailpipe.
Researching on Priuschat leads me to think I’ve got a bad head gasket but I’m wondering if I screwed something up when I did the EGR/manifold/plugs but I don’t think so. I’ve checked all connections and was very thorough in reassembly.

I have permanent codes P0403- egr circuit open, which seems to be a rare code and also P0300, P0302, P0304

Wondering if EGR is just stuck open, solenoid bad?- letting coolant into engine?

Should I replace EGR before attempting to do head gasket?

If you’re still reading this, thanks and if you have any advice or want to pass this onto another knowledgeable member, double thanks.

 

I bought the car with 34k.
This is the first EGR cleaning I’ve performed.

 

I’m down in the South Bay.
I am standing on the verge of gettin’ it on with the head gasket myself, if I can determine that it is the problem. The coolant disappearing and now consistent mis-fire at cold startup is pointing in that direction, according to @danlatu(). But this P0403 EGR valve open circuit code is making me suspicious that something else might be going on as well...
I’ve never done a head gasket. Is it difficult?
Fun? I enjoy a new challenge...
I am using OBD FUSION app and BLE device to monitor vehicle and get codes.
And all y’all here at PC to decipher!
Hey, we could all get together and have a head gasket swapping party!