Hello Adam,
If I understand your question, as you probably found there isn't a single geoprocessing tool that does exactly what you're looking for. It sounds like you have origin-destination pairs, and one (or more) weighted barrier datasets, which presumably take into account the ecological and oceanographic barriers relevant for your species of interest. You mentioned that you've tried to use R entirely to do this, but hit resource limitations. I don't know enough of the specifics of your problem to give you an exact answer, but here are a few things that may be relevant:
1. You can use the Cost Path tool with individual rasters and not do the entire CSV at once. Basically, you'd figure out how to do it once for a single origin-destination pair, then write a Python script (or use Model Builder) to iterate over the rows in your CSV, and run this analysis for each origin-destination pair within your dataset. Depending on the size of your raster and the number of OD pairs, this may take some computing time.
2. There are a variety of tools which integrate with ArcGIS which at least partially overlap with what you're asking. Circuitscape is focused on a single global optimization problem, but again could be used in an iterative fashion as mentioned above, and scales to quite large problems. MGET is another tool which is quite useful in this space, it combines R, ArcGIS and Python to solve complex modeling problems. It has tools, for example, for larvae dispersion.
Overall, it sounds like a general modeling problem, but if you post details we can try to help you through them. Depending on the size of your raster, you may also want to look at alternative representations of your connectivity dataset. For example, in the past I've used a pruned network model to represent global ocean connectivity at a relatively fine scale. Building this network initially takes some time, but the advantage is it then makes computing a route within the space very inexpensive and easily scalable.
Cheers, Shaun