To inspect the areas fully, or to weld in the brackets would need the removal of the engine and the body if you want to be able to do it right both from the necessity to be able to see the area under inspection and to thoroughly remove the coating from these areas or indeed to avoid damaging the body while welding..
If the coating is complete then it will prevent dye from penetrating so giving false negative results when looking for fine cracks. Conversely, where there is any deterioration of the coating you will get false positives as the dye penetrates between the coating and the metal. Mechanical methods of coating removal may peen over the very fine initial fatigue cracks so you would want to etch the surface after grit blasting or use a chemical coating removal method.
Magnetic particle inspection would be more appropriate since it is carbon steel but coatings can again give false results so you are back to removing the coating.
I'm not currently qualified in dye penetrant nor in magnetic particle inspection but have been qualified in both, have considerable experience of using both in some seriously awkward and difficult configurations and am frequently involved in major inspection programmes. I'd stick with thorough visual inspection for this application; albeit a bit more frequently than I have been doing mine! I will also stick by my previously expressed opinion that the crack propagation from effectively undetectable to clearly visible or indeed to the point of failure of the tube is likely to be very rapid. If I'm right then there would only be a very short window to catch a fine crack so probability would be against you finding anything less than a major crack. If a structural engineer wants to model the system and comes up with a long slow propagation I will happily stand corrected...