I had an almost identical issue (child is nearly 6, 15kg , just over 1m, medical issues etc) and I did a HUGE amount of research. The problem (as you've found) is that most pushchairs go upto a high weight, but not height. The special needs buggies don't tend to recline and so it's really tricky.
We went for the Phil and Ted's sporty online. It's got a much higher seat and my little one can lie down in it for naps. It's also very manouverable and good on rough ground. It's not perfect. It's heavy, it hates being folded, recline is faffy and it's not totally lie flat as the bit where the feet are dips down. In many ways I hate it 😂. But it's the only one that ticked our essential need boxes, which are similar to yours.
The next nearest (and opposite in terms of style) is the bugaboo butterfly. It got a surprisingly tall seat. It's folds down small, very compact, good for travelling etc. Downsides are the bugaboo price label, a relatively narrow seat, and although it reclines, it doesn't lie flat.
Neither come out anywhere near your price range sadly, but you may be able to get one second hand, which is what we did. For the Phil and Ted's, don't go for other models (some are smaller) and you want at least the v5 model. I tried an earlier one and the way the seat was sling made it non usable for napping.
We tried the the baby jogger city mini gt2, and it was smaller than it's dimensions suggested. Not suitable at all. The pop was what we upgraded from as it was too small - though it was an ancient model which may have been smaller.