Intermittent rough engine and misfires both in idle and while driving, codes P0305 and P0300

Also today I drove it. Cleared the codes, it rode good first trip not much issue I noticed. Did have a pending 305 Afterwards though. When I drove it back it was pretty much perfect, no issues. Was keeping an eye on the o2 sensors the whole time. After I got back home (25 miles or so) I let it idle as I kept looking at the data and the o2 graphs. It started sputtering finally and it actually stalled once as well. It fired right back up no issue. I will post some pictures of the sensor graphs as well.
Also I did a fuel pressure test with the new pump. At key on it was actually at 52-53 and at idle the needle was jumping upper 50’ and 60. I did notice the fuel pressure would start dropping as soon as I turned it off. Even from key on to off it would start to drop almost immediately. Not too fast but noticeable.

These are what the sensors looked like when it started sputtering after getting back.

This is what one looked like after first trip earlier in the day (idling).

Here’s what they looked like right after starting in the evening. Cold start.

And these are some while driving on the highway.

I don’t know if it’s just a coincidence or a reaction to what’s happening but I see the sensors oscillating a lot more rapid at a cold start then after it gets hot.
Trying to get you as much information as possible.

These are graphs of both upstream o2 sensors while holding 2,000 rpm's.

I do not have a vacuum gauge. Never used one before. I’ll do the dollar over the exhaust. Would it always happen if it were to get sucked in or just while the misfires are occurring?
It’s been mostly p0300 coming up lately. Also had p0304 come on recently as well but hasn’t come back

Will do.
Is a sticky valve something that happens only after getting hot and intermittent or would it be constant?

Okay, so gave it a shot and honestly not sure what it did. A few times while it was sputtering it felt like maybe it was getting sucked back a little but I was holding it tight to the tailpipe. Then if I looked at it closer while it was sputtering it looked like it actually pushed it out. I’ll have to do it again.
Also just to keep you updated first 20 miles I drove it today no issues I noticed. Towards the end of my trip it started up. Had some real bad stumbles at one point where it felt like it was trying to stall and jump back to normal. The stft did jump up real high while that occurred. After a few seconds it stopped and when I got pulled in I had the sputters on and off and started the test.
While idling I snapped the throttle a few times. I noticed the first couple of times I had some smoke or vapor come out the exhaust briefly. Wasn’t heavy and it dissipated quick. It happened a couple of times but then no more smoke when snapping the throttle. I kept it running and noticed the sputtering had pretty much stopped. I drove it up and down the street and didn’t really feel anything. Stopped and got gas and didn’t have any issues after restating and driving back. Kind of weed cause other times the sputtering would get worse and worse. Even would get some stalls. I did notice a strong smell of maybe burnt fuel if that makes sense from the exhaust and it was really hot back there.

PS, not sure if this is important or not but noticing when I get a check engine light whether it a 300 or 305 the freeze frame data shows that it went into open loop.

No sir, when I started it was pretty much in closed loop immediately. For example I took picture of the freeze frame data (I’ll post them) while key on engine off today. Cleared the codes then started the engine. I went right into live data and it was already in closed loop. I saw where the 300 code that I deleted was in open loop on the freeze frame and the pending 305 is as well.

These pictures are all the freeze frame data from the stored 300 code I deleted earlier.

And these are the freeze frames for the pending 305 code. It has not set the light on yet in about 40-50 miles with of driving.

And this is what the fuel trims looked like as soon as I got back home after 25 miles or so. Didn’t have much issue, a couple of stumbles here and there on the highway but nothing crazy and no rough idle when I stopped.
I hope I’m not over doing it with the pics and info. Thank you so much for your help! I hope we can get this fixed and the info can help someone else having this type of issue.

Hey Tom, thanks for the response. I’ve actually done multiple bottles of Seafoam treatment through the tank and have also done the spray treatment in the intake. Thinking about doing the spray again.