So...

I would suggest using a real hackamore. That would give you more pressure on the nose so the horse can understand what you are asking better. I wish I could give more advice, but I have limited use of hackamore bridles.

I don't really have the money to get a real hakamore and I like the one I am useing because it fits my horse well... amd she is an odd shape...
Liz

Did you buy that somewhere as a bitless?  Looks an awful lot like a halter.  Looks like there's very little pressure and it's all on her nose.  And it looks like you're sitting there not doing anything but still have quite a bit of pressure on her face.  Why?  I know she's a good girl so you don't have to worry but, if she decided to take off you'd have very little control.  The Dr. Cook's bitless has pressure points at the nose, jaw, poll and some in the cheek area....  You may be able to rig up something similar.  As for softening, you're talking about flexing?  I'd go back to groundwork to get her to flex and bend with pressure in the areas that get pressure with whichever bridle you use.

It is a headstall for a tie down, just with reins tied to the side instead of a tie down buckled to a girth.
 
As far as bridles go, I always like to use bridles for listening more than for telling.  The loose ring snaffle that you are using won't do any further damage to her mouth if it is used correctly.  When a horse is ridden in a heavy bit improperly for a long amount of time, the horse learns to balance on the bit.  This is why that horse is so hard to stop when you offer less pressure.
 
"Whoa" is a command that shoots through the whole body.  I have been known to spend full lessons on teaching people to "whoa" properly.  I have also been able to get on horses that are known for running through the bit to stop from the canter without any pressure on the bit whatsoever.  This means that "whoa" is a lot more than just pressure on the reins.  It is a shutting down through your body stopping the forward energy of the horse and holding it still.  Not to mention being able to hold your own balance so as not to throw the horse forward again.  Start with some ground work to get her attentive to you and make sure she knows the vocal command from you.  This will help her to learn to pay attention to your body when you are on her back.
 
Next, as far as lightness goes, I personally don't teach them to get light to the bit, but instead, I teach them to shift the weight backwards first, which naturally takes the weight off the front end and lightens the feel on the bit.  I want the horse to stretch into the bit and take a light contact, rather than come off of the bit as soon as I apply pressure.  At your mares age, this would take a lot of work to change her whole posture, but it is possible.  It would require a steady time commitment from you, which I know would be hard with you starting in college soon.
 
I know money is an issue, Dr. Cooks and many hackamores are a bit pricey.  So, if you are looking for something to just pop around the yard a bit and really don't want to use the snaffle, try a rope halter.  Prices vary, but you can pick one up in TSC for $11.  This will offer a little more feel for her.  Again, the proper way to go about all of this would be to help her with her posture and help her develop self carriage, in which case a loose ring snaffle would be just enough to offer a feel to her.  However, I understand that this is extremely time consuming and would take quite a bit of time and instruction.  Good luck with whatever you decide to do.