mesh--this is really important and good that you mention this issue.
I am going to explain the basic rule for assessing seat height and foot placement on pedal so that ones legs are at the most efficient position for muscle use and energy transfer.

put your pedal down at the lowest position, with crank more or less parallel to the seat tube, the vertical part of the frame that the seat is attached to (this tube is never straight up and down vertically, but angled)

put your heel on the pedal, the heel.
proper seat height is when your relaxed leg is straight (not forcing it farther straight) with your HEEL on the pedal.
When we pedal, we move our foot forward on the pedal, more towards the middle or ball of the foot, and thus our leg when pedaling will have a slight bend to it.

this is basically the most efficient position for best muscle use of our legs, allowing a proper extension and power from our leg muscles
a too low seat results in things being harder on the knees--in my lifetime of riding, I feel it in my dodgey knee when the seat is too low

your pedal toe straps being too small , as you described , your feet are too far back, and as well as having that weird claw foot feeling (I know what you mean, I tried some pedal cages that were too small years ago) your foot being in that position means that essentially your seat is too low and leg is not extending enough--bad for the knee muscles.

I've been riding spd pedals, mountain bike clip in pedals, for 30 years, but I do also ride flat pedals in the winter and on my commuter bike. If we move our foot more forward on the pedal, we extend our leg more. If we move our foot way back on the pedal, we shorten our leg extension--you can feel it when pedaling.

Sooooo- lets say your seat height was perhaps already a bit low (a common thing among people) AND your foot is back on the pedal as you described, you are not getting enough leg and knee muscle extension, and this is classic with causing knee issues.
A lot of people feel uncomfortable with a seat at this position because they feel they can't put their foot down flat on the ground when stopping, but toodling to the pub is one thing, when touring with a heavy bike you want the most efficient use of your legs and all that jazz.

its up to you to confirm all this blah blah blah, but if you are unsure, go to a trusted bike shop with serious riders, and get them to help you with getting your correct seat height, because as you experienced yourself, your knee felt better right away by allowing your leg to extend the proper amount.
Again, I personally have experienced the feeling you describe.

Also, being a big guy with big shoes, there are lots of pedals out there that are physically bigger, that have a much bigger platform, that you would probably benefit from, as it would spread out the pressure on your feet.
Generally with shoes, riding shoes have stiffer soles that really help with not flexing and causing foot and arch discomfort.
A lot of wider pedals are often expensive , but there are some reasonably priced ones too.
If you don't look into this, at least choose shoes that are the sturdiest and have the stiffest soles, it makes a difference for all day riding.

cheers