if the balance is off, however, lowering the stirrup and trying to stand up will invariably result in the rider needing to lean way forward in order to even be ABLE to stand. and, very likely, end up putting a lot of forward pressure into the stirrip, so it goes even further forward.
First to consider is if that saddle really DOES fit the hrose. if it isn't too narrow and thus propping up in front. that's task number one. part of that is having it correctly positioned on the back , probably sliding it back a inch or two.
next, consider the fit of the seat and bar position to the rider.
if the saddle fits ok, I'd do more riding without posting. lengthen the stirrups and do more sitting trot work. and, start your saddle search for a saddle that is better suited for YOU.