So you agree with MS and, for Candrakirti, a truth [satya] means an object, and each "object" is really two objects...
Not exactly, a truth is "an object of a cognition" -- you cannot leave the cognition part off since it is integral to the definition. A truth is not merely an object, it is an object defined as relative or utlimate depending upon whether the cognition is deceived or undeceived. One object, two natures, hence two cognitions, correct and false.
This is an development over the Abhidharmic concept of a truth, in which a truth [satya] is a cognition, for example, a cognition of water is a relative truth, whereas a cognition of the characteristics of water, limpidity, wetness and coolness, are ultimate truths.
In other words, here,in Abhidharma, an ultimate truth is defined as the irreducible cognition that remains after something (such as a cup or water) has been subjected to complete analysis.
There really isn't than much difference between this and the Madhyamaka definition. The Madhyamaka definition might run something like "...an ultimate truth is defined as the object of an unmistaken cognition that remains after something (such as a cup or water) has been subjected to complete analysis."
The emphasis in both causes, both in Abhidharma and Madhyamaka is on the cognition. So no, I do not agree with the MS discussion in all respects.