Transitioning from life sciences industry to consulting

Sorry if this is not super directly answering your questions, but here's my thoughts 

First, when I think of "life sciences" to me that entails a very specific set of industries (biopharma, diagnostics, things more at the molecular/mechanistic level) which is distinct from medtech which you seem to have your experience in. So first things first, are you truly interested in life sciences as I've defined it, or medtech? This is relevant because there are many specialized life sciences boutiques out there that specialize in biopharma/biotech (Clearview HCP, Clarion, ZS, etc.) and do work that often requires some degree of fluency and proficiency with biological sciences (mechanisms, disease pathophysiology, etc.) Often times, they will hire people with advanced degrees / some type of scientific background. Depending on what you studied at your "non-target" (in what world are CalTech, MIT and GTech non-targets lol), that may be a barrier at the resume screening stage and functionally for your success on the job as well if you don't have a decent biological science background. These specialized boutiques do not do that much medtech work. That being said, almost every large consulting firm (MBB, T2, B4) will have medtech and LS practices and those would be the obvious places to start your search at. 

Also what level were you at your previous roles and what exactly was your role? It's unclear to me if you were a consultant or corporate. At 350K a year, I'm guessing you were probably some type of AD, D, or VP role in industry in which case you'd probably be coming in as a manager or principal level hire. Your actual industry expertise IS valuable (for the medtech practice, less so for life sciences) and one track you could consider is the "expert" track that the larger firms have, where you will be hired into LT as an "expert" in a particular industry or functional area. Your 10+ YOE in the industry is certainly valuable and positions you well, but given I am relatively junior, I'm probably not in the best position to comment on what exactly a firm looks for in an industry LT-level hire / how to differentiate. 

Finally, I'm sure you know it is a very tough hiring market right now, so not sure how much these firms are looking to increase headcount. Doesn't hurt to reach out to connections or head hunters, but I would have tempered expectations there and understand that opportunities are hard to come by so there's less room to be choosy. In terms of what to watch out for, if you do get the role, it is well documented that it is notoriously hard for industry hires who are thrown into leadership roles right away. There are often steep learning curves for how XYZ firm does things, finding the right network and senior LT support, etc. and the leash is often shorter than you might think and many lateral / industry hires find a hard time getting up to speed and get transitioned out relatively quick. I say this not to scare you, but to help you understand what you are getting into and have the right mindset going in to set yourself up for long term success. 

Cheers