How could i get an invitation letter from authorized agency in china?

Good day! I already have an L type single entry granted 14 days of stay. I was supposed to travel 1st week of november to xiamen but was not allowed by immigration due to lack of supporting documents. My visa and ticket was arranged by a travel agency here in the Phil. but did not informed us about other supporting documents that we need to provide for the travel. This is supposed to be my 1st international visit mainly to visit a friend and his family. My friend shoulders all the expenses for me. I was supposed to stay at their place. Immigration was asking me to pass an invitation letter authenticated by philippine consulate in china. But my friend is having a hard time complying requirements. Instead,Can i just possibly get an invitation letter from authorized travel agency? Buy tour package for few days and spend the remaining days at my friend's place? Would this be a better option and could this assure that immigration would already allow me to go out of the country?