Unfortunately just going down long-side after long-side in shoulder-in just won't cut it. You've got to do something within the shoulder-in to encourage the horse to change the way he moves his body and influence him to take the outside rein. For some annoying reason they always just want to drop the inside shoulder and cross their inside hind leg underneath their body in a sort of poor leg-yield position, so we need to make sure they do the opposite - lift their inside shoulder up and step directly underneath with their inside hind to shift the centre of gravity further back.
I recommend doing transitions within the shoulder-in positioning. By doing a transition, you can use your outside rein much easier because you're either using it to bring the horse back a pace, or pushing into it by doing an upwards transition. The downward transitions prevent the horse running through the outside rein (you can do a strong half-halt with it to bring the horse back) and you can engage the horse by doing an upwards transition and pushing both hind legs into the outside rein with your seat and leg. Between the transitions you can also do 10m circles, especially if you feel you're losing the shoulder-in positioning and bend. Make sure you've got a good shoulder-in going on before you do the transition, otherwise the transition will most likely not be "through".
So how do you make sure you've got a good shoulder-in happening? Start by coming out of a corner or from a circle. Look straight down the long-side, but keep riding the horse's shoulders around the turn and keep that bend in their body until they feel like they are on 3-tracks. Use your outside rein to hold that positioning and use both seat bones to ride the hind legs forward down the track. The inside leg is by the girth, supporting the bend through the horse's body, and the outside leg is a bit further back guarding that outside hind from stepping out away from the line of bend. The inside rein has a soft contact keeping softness through the neck and inside flexion, and the outside rein is what holds all of this together.
Be careful you don't fall into the trap of letting the horse lean on your outside rein and escape through the outside shoulder. To test this, give a half-halt with just your seat and outside rein and bring the pace back for a couple of strides, or do a full transition. If the horse runs past this aid, he's escaping out of the outside shoulder. So you need do a good few half-halts with that outside rein to bring him back into balance and make sure you've got a bit of contact on the inside rein too - don't drop it completely.
If you're really struggling to get the horse to take the outside rein, keep using more and more inside leg and try to catch that energy with just your outside rein. Be really diligent in not using your inside rein. I guarantee you it will be ugly for a bit, but sometime things need to get worse to get better. The horse will get thrown off balance when you really push from inside leg to the outside rein and look for a way to rebalance himself. Make sure that way is by taking the outside rein and bending around the inside leg!