What would a Janissary suggest to be done to the Ottoman empire to fix problems that started the modernization?
One thing that must first be understood about your question is that Janissaries were not Ottomans (by birth). Janisaaries were soldiers who were taken as boys primarily from Balkan villages to serve the Ottoman Empire. As Eugene Rogan explains in his 2011 book, The Arabs: a History, the Janissaries were not often a problem within the political structure of the Sublime Porte. I do not believe that any modern Janissary (assuming that they were brought up in the same manner as historical Janissaries) would be a proponent of traditionalism.
I believe that it is safer to assume that a 19th century Janissary in an advisory position to the Sultan would actually work to speed and further develop the technological advancement of Turkey. If he were armed with the benefit of hindsight (as we certainly are today), he would likely be a staunch proponent of distancing the Empire from Russia and trying to engender more western learning. As the same author mentioned earlier (Rogan, 2011) relates, the Sublime Porte undervalued the lessons to be taught from Western curricula.
Furthermore, contemporary discretionary practices against Christians and Jews (who comprised most of the population who were able to skillfully translate western works into Turkish) drove these same people away. This crippled the ability of the Empire to stay current in medicine, engineering, and martial technology. The Ottoman Empire also had the disadvantage of not having a hinterland in any traditional sense. The less attended to provinces within it could have rightfully been centers of trade if they had been administered properly. Phillip Hitti (1965) relates a history of commercial repression and feudalism long after feudalism had faded into irrelevance in the West.
Overall, it's best to assume that a Janissary today would assume the same strategy that Turkey and the Balkans are assuming today; they would try to emulate the West in modes of governance and taxation/administration structures.