That’s a good question. Unfortunately, you probably cannot just deduct the six-month period. The federal Medicaid statute exempts transfers of the home to a caretaker child "who was residing in [the Medicaid applicant’s] home for a period of at least two years immediately before the date the individual" moves to a nursing home. The use of the word "immediately" would be the problem in your case due to the six-month gap. If you continued to live in the home for the six months your parents were in Florida, you would technically meet the residency requirement. The problem is that most Medicaid agencies also apply the "immediately" requirement to providing the care.
I would check with your local Medicaid office or a New York elder law attorney to see if they could provide an answer on local practices. Find an attorney near you today.