Trans-substantiation is a philosophical explanation of how bread and wine become the Body and Blood of Christ. And yes, it means that every muscle, sinew, bone, etc and flowing blood as well as the soul and divinity of Christ is present under the appearances of bread and wine. When we receive Holy Communion we receive God, Himself into our own bodies.
From Lauda Sion:-
"Hear, what holy Church maintaineth,
That the bread its substance changeth
Into flesh, the wine to blood."
St Thomas most certainly does not say the bread and wine do not cease to exist. 
The word 'accident' immediately implies car crash in most people's minds. In philosophy it has a totally different meaning. The 'accidents' of bread and wine relate to their appearance and one assumes that they are bread and wine.
However, at the Consecration this bread and this wine undergo a 'substantial' change; they become something that they appear not to be.
Your explanation is very near the Protestant doctrine of Receptionism.