To add to all of the great advise mentioned, your horse jumping flat, reaching forward with her nose and not clearing the rails at her back legs is an engagement issue, even though you say she is “quick, heavy and strong”, this is a deceiving thing the horse does that makes us (think) they are using their rear end, but in actuality, these are indications that she powers forward mostly with her front end.
For me as a Trainer when I read your post, I feel that 1) your horse needs to rebalance and engage from her rear, not with her front end and 2) she needs to be driven deeper to the take off spot and jump a bit higher by an inch or two to with a change in jumps to help her bascule…
IF she had balance brought back to her rear end, her “engine”, with a focal point on setting on her rear, then her mouth would be lighter and more responsive, along with a softer and more round bascule. To help with this first being how important it will be to the end result, she needs to understand (learn, re-learn or get more precise at) lengthening and shortening of strides at each gate, walk/trot/canter to have her respond to your requests for “extension and compression” at each gate so that she is at the exact pace and in your control at all times.
As for better jumping form, here are a few techniques…find a ground person who can adjust ground poles and fences for you to help with some of the following techniques… Have your ground person move the ground pole(s) closer in to the take off point if each round over that jump, a little bit one round at a time, until you are getting less of a flat jump. Power up your horse only right before the jump and put her deeper into the take off spot. This might not be easy especially if she has a habit of early take off points and jumping long and flat, so you might have to work at this. Take videos of her FIRST as you normally ride, then try compressing her take off spots, video tape that, study it before you go out to ride again next time, etc.
Secondly, it sounds like she needs to be set deeper into her take off spots at the jumps and lift higher with a bit of change to the jumps so she has a “curious” bascule that she is naturally going to clear for the purpose of the surprise. This exercise you can do at home by changing up some of your jumps. After your warmup on the flat, take her over a couple of jumps that you have changed up (a new surprise to her that are not her normal jumps). Don’t take her over ANY of her normal jumps, this exercise is for the element of new introduction. Have one or two set with an oxer higher in the front by a few inches with something new added to the jump she is normally not used to that she will see for the first time, something that will catch her attention but not move enough to spook her or make her refuse the jump. Take another two jumps and offset the angles. In other words, set the jump cups on one side higher that the cups on the other side, enough to make it appear awkward and uneven, with the height in the middle still the same. This is an illusional training method that helps the horse break the boredom of normal jumps and helps lift their legs and clear the jumps. Since we all know it is best to jump in the center, the offset fences not only help with horses to lift their legs and round themselves, you CAN ride your horse a few inches to the left or right each round depending on the height you want to clear. These offset fences I also use to help correct jumpers who come around tight tuns to a fence and want to slack off and assume they will jump just fine but end up tearing off the rail or mowing down the whole fence LOL. The fence to that inside turn is set at the higher height, making them set up sharper, back off from leaning in and clear the fence more clean and true.
I truly believe that once you have your horse more “in your pocket” than out of control, you will be more willing to give a release and have more opportunities to work on yourself. I would suggest just for now, focus on getting your mare back on her haunches, deeper to the fences, lighter and more responsive in her mouth : )