First, the backbone for SSD may need to be retrained on the higher resolution classification task. By default, both SSD300 and SSD512 use VCC16 trained on ImageNet images of 3x224x224. That will need to change if your dataset is sufficiently complex and the backbone does not perform well with the neck.
Second, using a larger feature map will increase cost, linearly I think. So double the feature map size will mean you will need double the VRAM and time to train/infer. Keep that in mind.
Third, the network architecture itself does not need to be change. If the input feature map is larger, the multiple scales of feature maps on which the prediction convolutions work will just be larger and should work still; the only difference is that the network will produce way more candidate bounding boxes for NMS.
Lastly, for your ValueError bug, what line was it on? There seems to be a mismatch of batch dims by |27|.  Is the error present for SSD300 and SSD512? If not, when does it appear? Only when you change input to 3x1024x1024? Try to use square FMs like 3x1024x1024 instead of rectangles like 3x1024x512.