After more through reading, it was brough to my attention that it would be impossible to use TSNE in the manner which I was hoping as the dimensions generated by TSNE is only representative of the training data. Further fitting with new data or transformation of data not within the training set would result in outputs that are not on a similar range and thus noncomparable.

I found a replacement to TSNE which is called umap. umap is also for dimension reduction but it can be fitted multiple times and data can be transformed along the same range.

I will explore umap and see if it will work for what I need.