this is the problem i have been working on with my mare. she has an endurance background so was used to baggy reins, any contact resulted in me being able to see her muzzle whilst on board. its a tricky problem but with time and patience i'm sure you'll get there.
It is brilliant you have already got a horse in self carriage (further than i started with) but to progress you do need contact, there are movements that just need rein contact to confirm what you are asking and if you go from no rein contact to asking something it will be a shock to the horse and the result will be a hollow horse.
Here is an exercise that i did with my mare last year and it really helped...
try picking up a contact in walk and just make sure that although it is there, there aren't any restrictions. make sure your shoulders move with the horses shoulders so that it is very rhythmic. i would also do a lot of circle work including spirals as this will encourage the horse to come up through the back and lower the head to be able to spiral but you will have a rein contact.
Go on a circle (20m ish) and ask for slight flexion to the inside, you only want submission of the head at this point and wait for your horse to just lower the head slightly, hold for a couple of steps then ask for straightness. then flex to the outside, wait until the horse accepts that the rein contact isn't harmful and relaxes into the contact, couple of steps and straighten. do this a few times. once you have established flexion of the head you can ask for a little shoulder in (remember this is all in walk to begin with) always trying to maintain softness but without losing the contact. you only need a few strides and then continue on the shoulder in curve to straighten as that is easier for the horse. do about a quarter of the circle straight (well with bend but you are almost straight on a 20m circle
). then do a few strides of shoulder out, then straighten (this way is always harder). at this point you have a choice, you can either try some hauches in and haunches out using the same method as shoulder in/out or you can change the rein and start with the head flexion and then move on to the shoulder in/out.
All of this will help maintain suppleness, it will help the horse understand contact of the reins and it is a good warm up exercise.
the haunches in/out is hard work for both horse and rider and trying to keep it on the circle makes it hard mentally but it will engage the back end more and helps both horse and rider concentrate on things other than the rein contact (although you need to keep thinking about keeping it
)
you can then do spirals with a bit of leg yield. if you did the hauches in you will find it is very useful for spiralling.
I would then progress to trot and would again just start with flexion of the head. make sure you have a very slow rhythmic trot and when you move onto the shoulder in/out (and haunches in/out) you will find it is much easier in sitting trot and the horse will need to collect and your seat helps ask for the movement.
If at any point your horse becomes stressed and hollows just calmly ask for straightness and then flexion and then shoulder/haunches in/out as it just make it easier. hope that helps