I had it occur for me in the UK marketplace. It was not necessary in the US because I had been on this marketplace for quite some time. The process should be the same though.
The process involved some message exchanges that ended up requiring asking for contact with a manager who contacted the fulfillment center.
I did not end up with as much oversized storage as I requested, but they did increase it.
The initial analysis is always based on the turnover for your stock. They did look for history that would support that the items could entirely be sold within 3 months (13 weeks). The request occurred after Christmas rather than before Christmas, after the annual Long Term Storage purge.
Based on other messages I have seen about oversized storage contraints, I would not expect you to get a positive response. I hear that oversized storage is already constrained and probably there is already demand that exceeds what is available from larger, better established, sellers.
All I can suggest is that you pull together reasonable and accurate forecasts with good math regarding your sales up until the end of October and what that would mean for Christmas (this should have reasonable assumptions on sales for November and December - separately).
You would then create a request and ask to get in touch with a manager soon after making the request to more formally discuss your needs over the phone. They may be able to help you get an exception. Odds are not good though for reason mentioned earlier.
A mitigation strategy could be for you to send in multiple shipments, perhaps weekly to keep you on a just in time basis to restock at a rate that is in line with your sales expectations.
Though it is logistically easier to ship the entire Christmas inventory in advance, if you need to live within your capacity, you can have new shipments ready to prepare (planned, but not approved) to get the capacity as items are sold.
After you have been on for more than a year, the constraints get relieved more quickly than you need, but that won’t help as much right now.
That might help.