Sending stuff off and hoping really isn't the ideal way to do it.
It's better to go there yourself with a box full of tools and parts, so if any issues are identified in a preliminary scan, you can try fixes there and then. if it doesn't fully fix it, at least you can do experimentation to see what things make a difference and eliminate things.
The only difference between a "pre approval" and a full approval is their level of liability ( and the cost).
It's usually exactly the same kit, facilities and staff. You can typically book a day or half-day and do whatever you can within that time - if you get it all sorted, the test results are just as valid.
This is especially useful if you have multiple variants or products, as you can test as much as you can in the time, and also be fixing one thing while another is being tested.
The only place I've used is RN Electronics in Essex
https://www.rnelectronics.com/ but I'm sure there are plenty of others