You see, parallel could mean that you have N Turing machines, one for each tape and they execute independent of each other. This is easy to achieve. You have a program that processes one tape. You can start multiple copies of that program, one for each tape.
That is apparently not what you mean.
One could have a "sequential" machine that executes one tape at a time:
FOR EACH tape
PROCESS tape |
What you did describe is equally sequential:
1 2 3
|
WHILE tapes have instructions
FOR EACH tape
PROCESS one instruction from tape
|
That is quite confusing, because consecutive instructions are in different tapes.
One cannot look at one tape and know what the machine will do.
One could of course preprocess/merge the tapes into single one, which is then fed into the machine.
Perhaps you have a valid idea, but you must describe its rationale.