The toe down does look natural and can come from a running background where toes down increases the stride length (same as bigger gear on a bike) or to get better pull up with toe clips without pulling out of road level of strap tightness. Here it looks like the raised seat to accommodate may be leading to choosing bars with less drop (might also be to get narrow) but as a side effect less reach causing the cramped position. Bike sizes do not seem to scale well with height so taller riders will be more cramped on the top tube than short riders, but with bars and stem there is room to go forward in the pictures here.
But as I mentioned - trying to change your natural foot position is not a trivial change and will take time to get used to. If it can be done it should help with higher cadences and reduced drag so may be worth a try.