I had the same issue trying to export a model with the Object Detection API, in my case I was using the model "ssd_resnet50_v1_fpn_640x640_coco17_tpu-8" from Model Zoo.
Basically, you have to:
Save checkpoints of your fine-tuned model.
Modify the "pipeline.config" file of the model you retrained in order to match the number of classes of your custom dataset; i.e, changing the value of "num_classes" properly (If the number of classes is not properly set, then the shapes of the graph won't match)
Use the exporter_main_v2 helper function to export the model for inference with the files you generated in steps 1 and 2.
I guess that you did steps 1 and 3, but not step 2.
I provide a detailed explanation of this solution in this notebook, where few shot fine-tuning on a custom dataset is performed and the resulting model is exported, loaded and tested.