Some progress with cold emailing - good or bad?

You need to provide your academic year, and it sounds like youre not networking but instead indirectly demanding for jobs last minute which won't end well. I would take the opportunity to build those rrelationships with those MDs for the next shot around for recruiting, and I would suguest you broaden the internship search for this summer because your about half a year late into the process.

Keep in contact with that MD. Perhaps even ask him to introduce you to the other members in his group, and get to know most of them. That way, when applying for the internship next year, you won't be coming in cold.

Thanks for your comments guys. However I don't take "wait for the next round" as an answer. Maybe I'll try to build a good rapport with MDs at elite boutique and subtly drop hints that I'm also looking for work shadowing or insight weeks. Going to focus more on smaller firms this summer.

PS I'm final year in a 3-year honors degree. Going to study for a master's starting in Sept.

I really need an internship this summer so I don't really have time to network

Do you even know if that EB is hiring? If so, then go ahead and fire away with your plan. Reality is summer is right around the corner and most firms (including regional boutiques) won't have positions open at this time of year. That's not to say it's impossible, but I'd recommend you revisit your current plan.