You have a great background so I am sure you are getting lots of invitations and deciding what to do next is challenging because of the choices. :) I think the value of an EIR gig will be contextual based on what you want to achieve. I took an EIR gig about 10 years ago and the purpose was for me to build a network, find a cofounder and accelerate funding to start my company. I think that things have changed a bit now with new funding mechanisms and the prevelance of social media(linkedin,quora, founderdating,etc.) which lets us network exponentially faster.
Firms have very different EIR programs too and how involved you get int the partnership/finance side varies quite a lot. I think you will definitely learn something about how venture works if you do take a position but i would clafiry that upfront.
I also think its better if you take these positions because you have a thesis of what you want to be working on and you are looking to improve the idea and find partner, customers via the EIR platform
There are great firms and great people out there that will become friends/partners you will have for life if you invest in it wisely so all EIR's are not created equal.
Happy to get on a call or grab coffee if you'd like to chat. It looks like you'd be someone great to work with.