By oval link do you mean lozenge? And what sort of pressure? Brakes? Keeping the head down? Accepting the bit? Turning?
A full cheek will help turning. For brakes, it depends. For a young OTTB I kept my bit and patiently, over months, as he grew more balanced it helped the running problem. If he has a habit of throwing his head up and trying to gallop off, a running or standing martingale could help until they learn how to support themselves in a better way of going. A clinician recently suggested an oval lozenge pelham with two reins. You can still use the snaffle rein but have a little more "umph" for back up with the pelham rein to get their attention.
I had the same problem, instead of a stronger bit I worked on more transitions and used more seat. She has a hackamore now.
They also have lots of advice about cheek variations as well! I hope this helped!
A mouthpiece with a lozenge is a popular choices; their rounded design allows for a comfortable feel in the horse’s mouth meaning most horses are more willing to accept the bit and the contact. The lozenge should lie central to the tongue. When a contact is taken up the lozenge allows the bit to fold in the centre and distribute an even pressure over the tongue and the bars without creating the ‘nutcracker’ action caused by a single join.
I found all of this on http://www.equestrian.com/equestrianbuzz/tips-advice/bits
They also have lots of advice about the
Maybe try a French link, a Dr. Bristol or a lozenge :)
The French Link bit is a double jointed bit; it has a small bone shaped link in the middle allowing the bit to lie flatter on the tongue making it a good option for horses with bigger tongues. When a contact is taken up it exerts pressure on the tongue and lips and is a mild mouthpiece.
Dr. Bristol: The Dr. Bristol mouthpiece has 2 joints which distributes the pressure of the bit over both the tongue and bars of the mouth using pressure on the tongue to encourage the horse onto the bit. The lozenge is a longer, squarer flat shaped lozenge centre piece is set at an angle therefore causing a sharper pressure on the tongue. The Dr. Bristol is not a great bit to encourage a contact however can be good if you need more brakes!