Yes, a Sept UY would work for the times you mention. With that, you have until April 30th of the following year to bank your points. This means any trips that take place through May would still be covered since you have to cancel at least 31 days in advance to avoid having all points for the reservation go in to holding. Holding points expire at the end of the UY they are in, regardless of whether they were banked points, current UY points, or borrowed points.
Sept UY's leave vulnerable June, July, and August. If there are your least likely times to travel, then that is what you want.
No UY will cover all the travel periods that is why there are some members who actually put up with having two memberships (different UY's) so they can cover their bases. We had two UY's at one point and I thought it was more trouble than it was worth.