My MVP will be done in a couple of months and I am looking for a healthcare organization to do the pilot for proof of concept. I would love some ideas on how to connect with these organizations and running a pilot in general.
You should call them up now before you finish your MVP but what you say to them is important.
If you say "I have this product that does ... ", most of them will go on the defensive because they know you are selling to them and you probably won't get anywhere.
If you say "I'm doing some research on ...", you are more likely to get engagement. Of course when you turn up, don't go into sales mode. The aim here is to interview them, conduct research, and build a relationship. Find out if what you are doing has any value to them. Then later on in the relationship, you can propose your solution where they have a say in what it does (co-creation)
For techniques on how to contact them, there are videos on youtube on how SDRs (Sales Development Reps) seek out prospects. Ideally, you want to get through to 10 companies a day resulting in one meeting a week. And "get through to" means working your way through all the receptionists/assistants/gatekeepers and talking to an actual user/stakeholder.
Unfortunately only you are going to know how to describe your ideal healthcare client and know who lands in the "perfect match" category. One would presume that before you started building your MVP, you already talked to many organizations like this, validating your marketing strategy and validating your product decisions. Go back to these same people with an invitation. Decide what incentive, related to your marketing strategy, will make sense progressing them through the pilot, and how they want to be rewarded for their feedback.
Your pilot is a time for listening mode. You should have a list of things you need answers to, but really you want conversations with 3 specific types of people: those who are installing, using, and administering the software. This will help you most with understanding the technical barriers to entry for future customers and give you a measure of ease of use, adoption rate, and total cost of ownership. You can make tweaks here, but this is not to instruct you on changes to your MVP. You have already tested your product market-fit by the time you're piloting software. Now you're focused on the experience of buying, installing, configuring, administering, and using the software. How user adoption goes smoothly, how customers are onboarded and supported, how the buying process is completed, these are the things that your pilot will be telling you.
If by some chance you skipped the product-market fit validation steps before building your MVP, that's very unfortunate. You will not be running a "pilot" but your validation testing, and that may require significant rework of your product.
You could try a smaller organization and offer them the software for free for piloting it for you. Being able to tell your future customers that you have clients that are currently using your software will be important. Make friends with someone there and they will be your referral for future customers.