I can squeak 10 days out of a 100gm gas bottle, but I switched to bars over porridge for that. So I only boil water for a coffee in the morning, and to rehydrate dinner. I don't get tempted by other people's evening drinks, as I much prefer not to have to get up during the night. I reckon you can do it as long as you protect the stove from the wind and don't have it cranked up. Be prepared to skip a morning coffee in dire circumstances. I had to do that once.
I've used a brolly now and then in more extreme heat, so I'd take it if there's that kind of forecast. But yes, it does tend to be windy in open areas of the OLT. I cover up with light, long sleeves and long pants and a good hat. A bit of sunscreen for reflected rays on face and neck when necessary. I don't think the brolly would actually make that any better. I pick somewhere shady for lunch if it's not cold.
I wash, love going to bed clean, but don't need a sink. Drop of eco-friendly 'soap' on a wet half chux. Other chux for towel. Repeat as necessary. Start with face!
Head net only 12 gm, but I've stopped bothering to ever take mine in Tassie.
Can't remember if you have access to a dehydrator. Toothpaste dots in a small ziplock bag, or a pinch of bicarb soda (also used for deodorant) should be lighter options.
I certainly have my own luxuries, that others would see as unnecessary. But I'll pop my 2c worth anyway, in favour of not needing the table. I do wonder how you'll fit everything in with the chair and table in a 45 l pack, but I'm sure you've thought about that! In case you haven't yet, it's worth loading up the pack with your expected weight, and walking a good long day with it, if you can't manage an overnighter. I love my Golite Pinnacle for travelling (hand luggage becomes a full size pack), but it just isn't comfy once I have more than about 10 kgs in it. I do much better taking my 1.6kg pack for multi-day walks.
I'd rethink the cotton bandana for pot (shake pot, and it's ok. Stove is in a zip lock bag, so no moisture gets in. Cotton takes too long to dry out. I use a chux for my tent, too, but see better option here: http://bushwalk.com/forum/viewtopic.php?f=5&t=28685&p=362771&hilit=wettex#p362771
Re weight of gaiters: I've used light and heavy ones, and I can't say I've ever noticed the increased weight when walking. Unlike shoes vs boots - where I've certainly noticed the difference. I now use shoes (achilles problem), which can be a nuisance in deep mud or off-track. But for the OLT, shoes would now be my choice anyway, unless I was expecting deep snow.
I confess that after some hypothermic episodes, I do carry a set of thermals to walk in that can get damp/wet on the bottoms, and a set of thermals for camp/night.
Large freezer bags or bread bags keep camp socks dry when you need to go outside.

PS Glad you're taking the PLB and bandage.