Speaking of the Commerce clause, here's a strategy Dems might try:

Slide into some bill that will pass a provision making a crime to intercept any internet communication or data with intention to use it to interfere with a woman's right to reproductive health. I'm not lawyer enough to write it all out, but this is the gist of the idea. Criminalizing the use of data crossing the internet to use against any woman or abortion provider in one of those state bounty-hunting cases. This could largely nullify those provisions in the state laws. (Granted, the kind of people who would murder abortion doctors wouldn't be deterred from stealing a little online data, but it could deter the vast majority of the hunters.) Small steps to take. Clearly, this is within Congress' commerce power.