No. The transformation problem has been addressed many, many times.
For one: Engels explains the "transformation of labour values into prices of production" as being a historical process that must be explained outside of maths. This is why he repudiated some of those who attempted to answer his invite to solving it with strict maths.
When there is a high rate of profit in an industry, capital moves to that industry. It overfloods the market creating a surplus, and the market price of that commodity falls from X to X-y. This new market price forms the basis for the cost price of the new commodity when its used as an input of production, and the cycle continues on.
As Marx says in Volume 3:
“As for the variable capital, the average daily wage is indeed always equal to the value produced in the number of hours the labourer must work to produce the necessities of life. But this number of hours is in its turn obscured by the deviation of the prices of production of the necessities of life from their values. However, this always resolves itself to one commodity receiving too little of the surplus-value while another receives too much, so that the deviations from the value which are embodied in the prices of production compensate one another. Under capitalist production, the general law acts as the prevailing tendency only in a very complicated and approximate manner, as a never ascertainable average of ceaseless fluctuations.”
The "problem" comes from the fact that gold rate of profit has to be "adjusted" to hold all equalities. This is a misunderstanding of what the average rate of profit it.
Again:
"What competition, first in a single sphere, achieves is a single market-value and market-price derived from the various individual values of commodities. And it is competition of capitals in different spheres, which first brings out the price of production equalizing the rates of profit in the different spheres. The latter process requires a higher development of capitalist production than the previous one.”
In other words, the rate of profit is not something "real" enjoyed by all spheres, it's a function of capital moving around through different spheres in search of a higher rate of profit. Capital overproduces, prices fall and capital moves on to the sphere with the next highest rate of profit. It's a continuous cycle, but does not interfere with the fact commodity producers are expected to produce certain commodities in a certain time (average productivity), and that the resources they consume are subject to these same social laws (this creates SNLT). The SNLT and laws that follow form the axis which the movement of Capital revolves around, obscuring the law of value, but never escaping it.
Not just market prices are modified when capital lowers the price of a good, but the whole structure of the market. Even if Marxist were to provide a mathematical fix (which has been done, many times over using many different interpretations), it would not do justice to Marx's mission which was to outline the most general tendencies of the movement of capital. The booms and the bust. We would be working with a limited number of variables, and modeling nothing.
And as Anwar Shakih has pointed out, there is no uncontroversial way to settle something like "the law of value". Marxian economics are held to a standard that no other school is held too, constantly being asked to justify fundamental axioms. Even Karl Popper would concede this is ridiculous.
Regarding the ECP, we had a thread about it recently. If you would like to attack my "word games" I welcome you to read my arguments and address them here. I also don't think you know what utopian means.
I will get to this later.