We use both a manufactured bridle, and we also rig half inch rope to a carabiner or steel/rated ring.

I have good luck avoiding cross loading by dressing and maintaing the carabiners constantly, not just prior to setting the system in motion.
Keeping slight tension in your system will keep the carabiners from going slack.

We use a system that was taught by Peak Rescue Institute for a class 5 raise or lower.

On the lower end of the stokes we use 2-adj litter attendant straps connected to a set of 4s by a triangular link. This connects to a SMC rigging plate. At the top of the stokes is a rope that is attached to the rigging plate by a figure 8 and goes to each side of the stokes at the head to another figure 8 attached with carabiners. Through the rigging plate you tie a long tail bowline with both your main line and belay line. These mainline longtail bowline then hooks to a Petzl Id attached to the attendant then terminated with a catastrophe knot. This allows you to rappel down on the stokes for better positioning. There is also a Etrier attached to the rigging plate that allows the attendant to use as a foot loop to move up and down on the mainline and take up slack on the Petzl Id. The belay line is then a direct tie in with a figure 8 follow through. The set of 4s is used to put the stokes vertical for the transition over the edge then you can raise the feet up once safely over the edge and put the pt horizontal. The patient has a pt seat harness on and has internal lashing attached. Then the patient is secured finally with external lashing.

I hope I have painted a good picture of what we do. I will try and find the time to set it up and take a picture and post it

Stay Safe

We use a bridle pre-rigged with 1/2" static kermantle nylon rope tied to an anchor plate. Each leg has a prusik cord tied to the leg and attached to each carabiner for adjustment. The down side I have witnessed with this type of setup for our department is that no one gets their hands of the equipment to learn how to tie this system and this section of rope does not get cleaned or inspected on a regular basis.