So i did exactly what you're doing, except I kinda got screwed over by my advisor in the 3+2 program. I went into a 3+2 program at Bloomsburg university of PA (program was with Pennstate engineering). I completed the 3 year portion and applied for PSU but was rejected. Evidently they don't allow transfers into the 3+2 program (I was at community college first). My advisor failed to tell me this critical detail, which left me kinda mad and lost.
So i decided to finish out my physics degree at Bloomsburg and apply to grad school. What I found was that grad programs actually really like to admit what they call "non-traditional" students... Students without a BS in engineering. I applied to like 10 grad civil (structural) engineering programs and got into my top 2 choices - Lehigh and Virginia Tech. I ultimately decided on VT and I'm glad I did. I absolutely loved it there.
I did need to take a year of undergrad prerequisites in order to start the grad program, so i was there for 3 years (I did research, so my MS was 2 years instead of 1). Word of advice: if you're looking for funding, look into teaching intro physics labs! Easy money and free tuition. And Virginia Tech was desperate for GTAs, since they have 1000+ new engineering freshmen every year but only a very small physics department. I didn't find this out until the semester I got my research, so I was only able to be a GTA for 1 semester. As for prereqs, I feel like I would have benefited from taking some extras beyond what was required. I find myself a bit behind others in some respects - predominantly with other disciplines of civil engineering outside of my own. I feel very confident in structural engineering based on my education.
I didn't have a stellar GPA at Bloomsburg, but i managed a 3.78 at VT and had 3 publications to my name thanks to my research. I thought I was well positioned to get a job offer, but I still found it quite difficult to even get an interview or a call. I can't say for sure whether or not this had anything to do with my physics background, but most others in my department at BS+MS in civil engineering, 1 or more internships, fantastic GPAs, etc. A lot of them got multiple offers pretty quickly, so it was tough getting no interviews for several months. I was actually on the verge of bankruptcy when I finally got an interview and a job offer. But take this all with a grain of salt, because I graduated in 2011/2012 and the job market was still recovering from the recession.
Getting your foot in the door is the hardest part. Once you do that, you can hop jobs without the stress of not being able to pay bills. My first job was for a DBE (Disadvantaged Business Enterprise), which meant they got really crappy work given to them from bigger firms. The work sucked and was primarily bridge inspections, but the people were nice. I jumped a couple more times, and I've been with my current employer now for over 8 years. I feel like a regular engineer, like anyone else here.
As for the FE & PE, NCEES is pretty vague on how to handle these situations with non-traditional students. After a lot of digging, I found out that your MS can count as the qualifying degree that enables you to take the tests, so long as the school you got your engineering degree in is accredited at EITHER the graduate OR undergraduate level (they cannot be accredited at both, so most schools try to get their undergrad program accredited). Virginia Tech is accredited at the undergrad level, so even though I only got my MS there I was still able to take the FE & PE. I've been a PE now for over 6 years. When you only have a MS in engineering, the MS does NOT count as 1 year of experience. That policy is only for engineering degrees you get after your "qualifying degree". Now as for NY State, you'll have to do a little research to see if they have any special restrictions on degrees. I'm inclined to say no, but if you're in civil engineering it wouldn't surprise me if they're more strict, given... Manhattan. With that said, I'd encourage you to consider the fact that you may not end up in NY in the end anyway. Beggars can't be choosers. Im from PA but i ended up in MD for 10 years. I only recently moved back to PA by transferring to my company's Philly office.
So to summarize, the 3+2 might help you get into grad school easier but it might make finding a job a little harder. This is pure speculation though based on my experience. I wouldn't consider it a hard rule by any means, just something to think about. Try to take more undergrad prereqs than required. Unless you got money, look into getting GTAs when you get to grad school.