The startups I'm aware of that have done this have started by approaching individual doctors to gauge their interest and give them demos and/or MVPs to try out. If that works out, they contact those in charge of purchasing. This is certainly not any easy approach though, doctors are constantly getting approached by startups with some new app that they want to be tried out. Keep in mind that doctors already have a complicated workflow, and something that you might think will make their life easier, will in reality make it more complicated and lead to more problems. Also, there can be a lot of red tape.

One company I mentored had an Indian cofounder, so they went to India to get into hospitals more easily. The regulations on medical equipment are far more lenient than in the US, and also they are more open to trying out innovative and affordable solutions, so it's easier to get new things into hospitals, and to alpha / beta test ideas there (as long as it's not something that could cause patient harm or death).

I haven't come across any startups that have gone the tech integrator route, but if you've unsuccessfully tried the other option a tech integrator could be a great idea.

Let me know if you'd like any more detailed advice based on your specific product,

best,

Lee