When I'm stumped by lack of loading data for a wildcat that has no published data is to find another case and caliber as similar as possible. In this case you are lucky, the 6.5 X 300 offers a lot of data. I would take a particular bullet weight and compare it to the 6.5 X 300. Take the starting load for that bullet weight, reduce it by another 5% and you have a starting load for your .257 X 300. Take your time using all the tools you have at your disposal. A good chrono is indispensable. A good Micrometer to check expansion at the base is required. Keep an eye on your primers for excessive flattening as well as the case head for any flowing.
As always when sailing uncharted waters, take your time and keep notes. I you come across something that doesn't look right, BACK OFF! Common sense and good loading practices are the watchword. Good luck on your first quest in the wide world of wildcats. I hope others will join in and suggest any thing I may have overlooked
The watchword is BE SAFE.