Hmm, not the blade expert here, I know others will have better input, but I wonder if your slipping has anything to do with the combo of older boots and blades. Is it possible that in addition to having blades that may be at the end of their life the boots are also giving you less ankle support causing more instability? You ask if your edges are too sharp, IME if the edges are too sharp you see trouble with the blade digging deeper in the ice than you are used to, so you might have trouble with stopping, spins, turns, but not necessarily holding a landing edge. Another issue you may want to consider is that if you do not have your blades sharpened regularly and often, the difference when you finally do have them sharpened it can dramatically affect your skating. I feel the need to get mine sharpened about every 20-30 hrs and try never to go beyond 40 hours, At that frequency, a fresh sharpening just feels good, no major change in my abilities one way or another.
I know that for me and most of the people I skate with, having a good, consistent blade sharpener, and also knowing your ROH (the "depth and hollow" you are referring to) is pretty important. It is kind of surprising to me that the person you were talking to was using the "the fingernail test" (not always accurate) and not talking in specifics of Radius Of Hollow...it sounds a bit hokey for a supposed expert in blades. There are some good articles online explaining ROH and why some work better for some types of skating. You are trying to strike a balance between edges deep enough to hold but shallow enough to be able to turn. Different types of skaters have different priorities as they get better. I think it is helpful to know your ROH and know that you may want to change it one way or another to assist your skating over time.
At this point I would check with your coach when you can on the condition of your boots possibly contributing to the problems and also, if you trust this blade guy is right about your blades being at the end of their life, look into getting new blades. If you are not confident in his assessment, take them to a different person and see if the verdict is the same on the need for new blades.
Btw, if you do get a newly sharpened pair in the future that is just too sharp and grabby into everything, you can dull them a bit with a Honing stone. I always keep one to smooth minor nicks, they are a nice tool to have.