Changing number of items included in package on single ASIN

Hi all, I have a self branded product selling through FBA. I’ve gained some good traction over the last year, and now in the past month I have seen a few other sellers create very similar items to mine under their own branding, but they are offering one additional piece in their package than mine do.

The trouble is, now some of these new competitors products are showing up in the compare to similar items section on my listing. I have much stronger branding, especially for the market I’m after, but I’ve noticed a decline in sales over the past week

Am I able to change the quantity of pieces included on an ASIN? I have debated creating a new ASIN with new UPC, but I have several inbound affiliate links that have been helping drive my sales and I can’t afford to lose that.

My plan would be to:
1 – Change my packaging and include the extra piece.
2 – Wait for my FBA inventory to reach 0
3 – Immediately Send in the new inventory
4 – Update the listing to include the extra piece (currently I don’t even have this attribute, I only have it in the description)

Will this work? The only drawbacks I see are my items probably being unavailable for a few days, and if I have any returns of old stock that get put back into inventory they might get shipped back out (I only have a 1.5% return rate).

Anyone else gone through a similar situation?