1. Closed versus open: yes that is interesting! I like M50, but they still sound like a headphone, somewhat closed proximity sound: it is hard to explain, but being very aware they are headphones. Hoping to open up the sound with the HD600, 650 or 6XX as time will tell.
HD6xx line isn't going to make for an "out of the head" image, in fact that entire range is not even in the radar for gamers. What they're good at is relative positioning, ie, you don't get anything too abnormal that headphones fail at vs speakers like having the cymbals too far forward and to the flanks like the drummer has really long but fast arms, but they're slightly more proportional. Angled third party earpads will not help either as they'll just push those same cymbals closer to the center and a little bit to the rear, where they should be, if you shrink the image to a mostly in-head size and keep everything proportional. You gain some depth here but it's not going to be anywhere near what speakers do when it comes to imaging. Same thing with Crossfeed, which basically tries to emulate how both ears can hear both speakers as they interact with a room, except instead of just filtering everything across both channels and basically just making for bad levels of crosstalk, Crossfeed has variable gain and high pass filters. Filter higher frequencies across both and you push the cymbals to the back, as they should be, but also closer to the center because proportionately your drummer should be around the same size as the rest of the band, but some interpret that as "narrow" soundstage and consider "wide" when the cymbals are disproportionately set wider than where the rest of the instruments are.
At minimum you've got the K701 which projects a wider and deeper, ie overall larger, image with more of the soundstage in front of your eyes, but evne the K702 isn't that much better when it comes to bass. Then the K7XX and K712 ditched their angled earpads because people too used to headphones instead of speakers complained that everything seemed unnatural. Past that there's the HD800 and HD800S, and to a lesser extent maybe the Beyer T1 and a few others.
If you really want to go all out on simulating speakers on a system the size of a headphone, just save up and pray you get lucky and come across a used AKG K1000, plus a good amp to drive them (you can get any 10w to 15w Class A speaker amp).
They basically mount at the same general direction speakers would be, except they're still on your head, with a similar toe-in angle, and both ears can hear both speakers just like actual speakers.
2. I will be checking out other options for recommendations. Let me say this: I AM biased, I have to admit. I have several cheap CX2-- and CX4-- IEMs that I love the sound of for gym or other activities. So I am partial to Sennheiser brand.
If you want a more out of your head sound there's the HD800 and HD800S.
3. HD650 is definitely $100 more and outside the budget. However, I see they are almost identical to MassDrop 6XX which I literally missed by a few days. Do you know how often these come around? I can wait, but maybe not for a year.
Well these aren't exactly the best for your goal of out of your head sound, so you can just save that money now, and keep saving, and saving, and saving, and saving, and saving, and saving, and saving, and saving, and saving, and saving, and saving and eventually you might be able to get an HD800 or HD800S.
Or by that time something new has come out that can give you what you're looking for for less money, without requiring you to blow even more money on an amp or at least can easily get away using a less expensive one. You never know.
4. AMPs: those sound good and I've been doing some reading the HD 600 respond very well to Vali2 because it does have a tube. The NFB 11 looks awesome! However outside my budget, again.
Maybe totally out of the blue, but what is the opinion for a used Matrix M-Stage HPA-1? I can attain for about $130 shipped. This setup of course still be using the UCA202 RCA output into the amp.
If you start saving for an HD800 now, and assuming no new developments in headphone technology (that isn't DSP) by the time you can get one, then you can get the HD800. And then maybe drive it with a Darkvoice DV336se fed by something like an ODAC.
Alternately, if you want a shorter wait, maybe save up for a K702 and a Schiit Asgard+any decent DAC (ex Modi) or an AudioGD NFB-11.