Hi, Welcome to JustAnswer.com, I am glad you are here! My name is Eric & I will endeavor to answer your question.
At face value, I think you have a pretty good idea and it sounds structurally sound. That would sure beat tearing out your existing concrete! It is possible though that because this is an unconventional manner of supporting your deck, if you intend to pull permits and get inspections, you may need to get an architect or engineer to sign off on the plan. You also however, might be able to draw up the plan yourself and submit it when you apply for your permit. The city plan reviewer himself is either an architect or an engineer and might just look at what you have drawn and say OK, build it. If there are any minor changes he wants to see, he may also just notate on your drawing somthing like "Add Simpson HUC hangers here". I have been successful in getting my own "unsealed" hand drawings approved by building & zoning many times and that is in Miami-Dade County one of the toughest building departments in the country. Worst comes to worst, you submit your drawings and they reject it and tell you that you need a sealed plan.