Disclaimer: This is my opinion which may not be shared by the majority of surgical program directors. The questions are italicized.
Is there a way to find programs that don't have Step 1 cut offs? No.
Should I email them my 230 on the USMLE practice test? That would be of no use.
Should I explain my situation or will that seem like a sob story? I've had bad luck but just a string of it and I feel like it would sound like I was making too many excuses. As I read your story, it did sound like too many excuses. The problem for you is that there are numerous other candidates out there who don’t have these issues and have better scores.
Should I strategically book rotations during interview season and hope they decide they want me (does that happen and do you have any tips on this)? The value of so-called “audition electives” is controversial. I never put much stock in them, but I think many program directors do. If you decide to do some audition electives, you should focus on smaller community hospital programs. Many programs list where their residents went to medical school on their websites. You should pick places that have taken US IMGs recently.
Should I just take my time and apply late with a killer step 2 score? Or is applying late even worse? Those are tough questions. It would certainly help if you can achieve a much better score on Step 2. I think it may depend on how late you apply. It seems that programs are scheduling interviews earlier and earlier and interview slots might be filled if you apply late.
A Step 1 score of 200-210 is not necessarily fatal. Based on recent NRMP data, I would say you have a 10-15% chance of matching in surgery. Read my recent update on the residency prospects for IMGs. Here’s the link. As I noted in that post, a lot depends on which school you are attending. If you are at St. George’s or Ross, you have a much better chance than if you are at a lesser known offshore school. You should check with your school to see how many of its graduates have matched in categorical surgery.
Try to obtain letters of recommendation from surgeons who might be known outside of their own hospitals. If they can contact program directors by phone to personally recommend you, it would be a big help. As you correctly assume, many programs simply do not look at applicants with USMLE Step 1 scores below certain cutoffs.
The only thing you can do at this point is to excel in your surgical rotations and electives, get a good score on Step 2, and hope that your letter of recommendation writers can help you. Send out applications (as many as you can afford) to community hospitals and see if you get any interviews. Regardless of the number of interviews you are offered from surgery programs, you should have a backup specialty in mind. You could consider accepting a preliminary position in the supplemental match, but be aware that it may not lead to a categorical spot in the future.