You can use any state of the art object detection such as DETR, EfficientDET, YOLO etc. since they have an object 'person' in them. But, if the density of people is high in the images, then, you should look at 'Finding Tiny Faces' which is good for that problem (this will help you detect faces only, think group photos). If you want to find the whole person ...
You can reduce your photo size and scale the corresponding boxes to the new dimensions (416x416).
Or if you want to go with your technique, you can slice the image and then, check if the bounding box lies in the slice, then, reorient it according to the slice you took.
Take a look at albumentations library for this.
Unfortunately, the answer here is that "it depends". People have taken different approaches to this problem and I'll describe a few here. None of which however is the "right" answer.
When generating benchmark datasets, we actually do have this problem. To be honest, most of the time the labeling is done to the best ability of the ...