Why would anyone want to set Firstfruits as the 16th of Aviv?
http://www.fivedoves.com/letters/march2009/ola326.htm
The 16th day of Aviv has no basis in scripture.
Regardless of when the first day of the month of Aviv is, the morrow after the sabbath remains unchanged.
 
Leviticus 23:11 says that Firstfruits is to be on the morrow after the Sabbath.
 

"And he shall wave the sheaf before the LORD,

to be accepted for you:

on the morrow after the sabbath

the priest shall wave it."

 

The 14th was Passover and the 15th was the first day of Unleavened Bread.

Leviticus 23:7 says the following about the first day of the feast of Unleavened Bread.

 

"In the first day ye shall have an holy convocation:

ye shall do no servile work therein."

 

Sounds like a sabbath to me, but then we have to ask; Why didn't YHWH call it a sabbath?

He didn't have any problem calling The Day of Trumpets a sabbath (Lev 23:24) and the Day of Atonement a sabbath (Lev 23:32) and the first and eighth days of Tabernacles sabbaths (Lev 23:39).  Why didn't He call the first day of the feast of Unleavened Bread a sabbath?

Could it be that He didn't want to confuse the issue of Leviticus 23:11?  Had he used the word 'sabbath' in Leviticus 23:7 and 23:8, would the reader be confused as to which sabbath He meant in Leviticus 23:11? 

In His declaration of His feasts in Leviticus 23, the only place the word 'sabbath' is used prior to verse eleven is in verse three, where He is describing the seventh-day, weekly sabbath of rest.  For that reason alone we could conclude that the 'sabbath' spoken of in verse eleven is the seventh-day, weekly sabbath of rest.

Clearly, the nature of both the first and seventh days of the feast of Unleavened Bread identify those days as sabbaths, but the text doesn't call them sabbaths, and I believe that it is for the above reasons.

Jesus rose from the dead on the first day of the week, the day we call Sunday.  All four gospels say so.  Paul said;

"But now is Christ risen from the dead,

and become the firstfruits of them that slept."
 

As His death was foretold in the symbology of the Day of Passover, so too was His resurrection fortold in the Day of Firstfruits.  He was crucified and died on Passover, and He rose from the dead on Firstfruits, the first day of the week, the "morrow after" the seventh-day, weekly "sabbath".