^^^Well, the pics should be posted on this thread. Or feel free to start a new one. Hopefully, LevelHeaded and BBB will be able to look at them and offer some insight.
My skill set centers around designing training programs so that people are able to train AROUND their injuries and not through it (which, we should all know by now, is playing with a loaded gun).
I think stretching the upper traps for at least 30 seconds to activate the golgi tendon organ is an important part of doing exercises such as Y's. Yes, performing SMR before each set can be unrealistic in a commercial gym setting. However, the static stretching can and should be performed for people who need to down regulate a certain body part so it doesn't conflict with the exercise.
At this point (and I'll repeat this at the end of this post), I strongly encourage you to research other specialists in your area (as well as post pics here). It sounds to me like the first doc you saw is either incompetent or didn't really care.
As for the exercises you described, here are some possible variations:
db press (if you can use a slight incline, that might work best - avoid flat bench)
push ups using perfect push ups, blast strap, or something similar (add external load using weight vest, bands, chains, or even McGyver a cable station).
one legged squats off box. don't laugh at these - they are surprisingly effective with a 3-4 second eccentric. also, if you have access to bands, use them to sit back and make the move more hip dominant vis a vis vertical tibia when in the hole. once you get over the learning curve and any preconceived notions, you will be AMAZED at how hard you can load the legs while sparing the spine.
For example, I am currently experimenting with a protocol in which my lower body work consists primarily of RDLs (uni and bi) and one legged squats. For speed (because strength without speed makes for poor athletes), I rely on power cleans and some med ball work (the light weight of a med ball addresses the absolute speed end of the strength-speed contiuum). The RDLs and power cleans taxes my spine and CNS pretty damn well. So, in order to get in sufficient volume, I took out the traditional squat and front squat and replaced them with the one legged box squat. I perform this with a 5 second eccentric, 1 sec pause in the hole (below parallel but NOT sitting on my calf) and concentric as explosively as possible with out losing form. I work up to max triple, then do more rep work using bands. The bands really allow you to sit back (which the free form version doesn't allow). This is important because, although quad dominant squats (tibia past vertical in the hole) is an important part of athletic movement people need to spend time in hip dominant squat patterns as well (tibia vertical when in the hole). This will minimize the possibility of any future knee issues AND help to teach proper glute activation.
In fact, I start off all my beginning or rehabbing clients with hip dominant squat patterns (unless they have specific contraindications) and integrate quad dominant squat patterns as they advance. Show me a trainer or coach who has beginners do walking lunges from the get go and I'll show you an idiot.
This is an example how proper programming can allow continual improvement WITHOUT aggravating past injuries or creating new ones. It can be done IF you are willing to flush preconceived notions regarding what is and what is not weight training.
I see all these threads in this or other forums about how people drink the 'bench, squat, dead' kool-aid without a proper understanding of the fundamentals. (Sadly, many of the writers on this site do not help matters because they themselves preach it.) Well, guess what...many of those people either end up posting on the Injured forums or lurking. That should speak volumes.
I'll repeat my advice to post pics on this thread or to start your own and to start a search for a specialist in your area. Your case most likely involves more than over active upper traps (although that certainly appears to be a contributing factor).