Bluespook, oxidation is quite real. If you take a bottle of Madeira wine or Sherry and smell it, you'll know what oxidized mead or wine starts to smell like. In some cases it can actually be desirable, but most of the time, it is considered a major flaw. It can be prevented by limiting exposure to oxygen and avoiding high-temperature storage.
#1. The size of the primary is irrelevant. Bigger is better. Bigger means never having a problem with MEAs and having to mop up a big mess. In a closed container, an active fermentation will absorb and bind up the oxygen, and the large amount of CO2 produced will chase out any remaining oxygen, nitrogen, and other air components. As noted above open fermentation can be done, and while the yeast are active, you won't develop the oxidized aroma.
#2. Leaving mead in a HDPE plastic bucket does not protect it from oxygen. The HDPE plastic allows oxygen to pass through so even if there is no headspace in a bucket, the oxygen absorption will continue. With that said, there are some folks who age batches long-term in a bucket. BrewBoyTrev over on the Northern Brewer forums has done this with success. He has done it with fruit as well. I'm not yet convinced enough to recommend this approach, but if you try it, I hope you'll post up and tell us how it goes. Perhaps you and Trev can teach us all something.
#4. Ascorbic acid will not prevent oxidation. In wine trials where they have used it with white wines they actually found that bottles treated with ascorbic acid actually has a faster rate of oxidative browning than occurred without ascorbic acid. I'm not sure of the mechanism for this as ascorbic acid is an antioxidant, but in practice, it interacts with other components in wines to create more oxidation. Sulfites work better to prevent oxidation in wines (and we presume in meads as well).
There are several ways to deal with headspace after fermentation is finished. This thread
One other suggestion I'll make is to consider shortening the time you leave the fruit in. With fruit pulp in the lees, there is a higher risk of developing sulfur odors. Secondly, excess time with fruit pulp/seeds often extracts bitter tannins and vegetal odors. Most of the good stuff (aroma and flavor) that you want from fruit will be extracted by an alcohol solution (mead) within a few days (7-14). Beyond that, you aren't getting useful stuff, but may be getting the problems I mention. With this in mind, you may be okay racking onto a fruit in a bucket as a secondary, and then transferring back off the fruit into a carboy after a few days.
With melomels, I find oxidation really can occur quickly and I try to protect my fruit meads with sulfites and limited air exposure. Traditional meads seem much more robust, and less prone to oxidation. Many people will keep a traditional mead in a container with excessive headspace and have it turn out fine. Nevertheless, with enough air exposure, you can create oxidized, sherry aromas in mead - done that.
Perhaps an even bigger concern than oxidation is the chance for spoilage organisms. Acetic acid bacteria need oxygen to grow. Sulfites will not stop them. Alcohol levels in most meads will not stop them (they can grow in 17% ABV). The only thing that will reliably stop them is having no oxygen. There are other spoilage organisms that also like air, and the best way to prevent them is make sure there is no headspace full of air.
I hope that helps.