(There's a separate issue — which was actually the root of the original discussion — about whether announcing the Hugos at conventions over Easter is better than issuing a press release on a Tuesday (the best day for press releases) in a non-holiday period, but that's a different discussion. As usual on THLTSNBN, the discussion drifted away from the original question.)
In my opinion, no matter when you set the deadline, you will still have many people complaining that they didn't have enough time to evaluate the previous year's works. So the question becomes "how much enough to satisfy most people?"
I've suggested that instead of the default eligibility period being the previous calendar year, we make the eligibility year run from September 1 through August 31. Stuff published in the fourth quarter of the calendar year N would be eligible at Worldcon N+2, not N+1 as it currently stands. Furthermore, I would prohibit nominations from being accepted prior to February 1. (This last dovetails with the current requirement that you be a member by the end of January to nominate and would slightly simplify voter administration.) This would guarantee a minimum of four months of "evaluation time."
One bad thing with this proposal is that it means that works released at Worldcon when Worldcon is held on its traditional first-weekend-of-September dates wouldn't be eligible at the following Worldcon, but would have to lay over another year. This can be solved in the simple case by running the eligibility year October 1 - September 30 or by a more complex formula based on the actual dates of the Worldcon, although the latter would lead to the eligibility year varying between 11 and 13 months.
Do I think this is a good idea? I'm not sure. I am sure that it would complicate the Adminstrator's life because it would probably make it more difficult to determine whether a work was published in the correct period. Some works only have a year of publication, not a month. (For instance, works published with no stated publication date only have a copyright date, which is a year.) The current calendar-year system is easier to administer at the expense of possibly penalizing works published late in the year. Or maybe not, since works published early in the year sometimes are forgotten by the time next January rolls around, and this proposal would exacerbate the problem.
I expect the proposal would significantly reduce the credibility of the "I didn't have time to evaluate the works" complaint, although it will never eliminate it entirely.
Should anyone really want to take up this proposal, I'll draft it in the proper technical form for you. I don't expect to introduce it myself.