Shelamim of Simcha And Chagigah

The Gemorah in Pesachim (70b-71a) brings a machlokes amoraim if one can fulfill the obligation of shalme simcha with animals that are slaughtered prior to the holiday or do we require זביחה בשעת שמחה.  We see from the opinion (עולא אמר ר"א) that requires זביחה בשעת שמחה that the mitzvoh isn’t fulfilled by the eating of the korban, rather there is an obligation of the holiday simcha is to bring a korban.  The language of Maimonides indicates this way as well.  He says in positive commandment #54 and Laws of Chagigah 1:1 the mitzvah is to be מקריב  a korban.  On the other hand, the Gemorah in Chagigah 7b says that one can fulfill shalme simcha with other korbanot.  If one needs a הקרבה as a shelamim, how can one fulfill their obligation with other korbanot? 

Tosfos in Chagigah says (in one answer) that one can fulfill shalme simcha with נדרים ונדבות only if they are offered לשם שמחה, not לשם נדרים.  We see from Tosfos that one does need to offer the korban for the sake of simcha in order to fulfill the הקרבה as a shalme simcha.  On the one hand you don't need to offer a specific shalme simcha, but you do need to have intent that the korban is being offered for simcha (see Maadanei Moshe siman 4.)

However, Rashi in Zevachim 99b explains that you can use a todah as shalmei simcha only because its called a shelamim.  Why does it have to be called a shelamim if you can fulfill your obligation with other korbanot ?(see Sfas Emes.)

What is the din regarding the shelamim of chagigah, does it have to be offered on yom tov itself?  The simple understanding would be that it has too because it is an obligation of the day.  That is the view of Tosfos in Pesachim 70b ד"ה שלמים as well as the opinion of the Rid (71a).  It is clear from the Raavad and Rambam Laws of Chagigah 2:10-11 that they disagree.  How can they hold you have fulfilled your obligation of bringing a korban to Hashem?  We see that they must hold the obligation of the chagigah isn't to offer a korban to Hashem, rather its an obligation on the person to eat 'לפני ה.  Hence, even if the הקרבה  was done before the holiday, since the eating itself is done on the holiday one fulfills their obligation.  Tosfos on the other hand, holds its an obligation of הקרבה and therefore, the הקרבה must be done on yom tov (see Avnei Nezer #422 and Maseas Moshe siman 97.)