Kristen - buy one of these: http://www.rei.com/product/401068/open-country-4-quart-pot-with-lid#reviewsTab 4 quart aluminum pot, 1 lb, $17.95 - well worth the time it will save you melting snow. There is also a 2Q pot, but 4 is really a lot better.
Here are some snow anchors as well: http://www.rei.com/product/725165/rei-snow-and-sand-tent-anchors#reviewsTab
(bring regular tent stakes as well, you may be setting up on either snow or earth.)
If the weather forecast is for decent weather you might consider leaving the vestibule behind. It would be nice to have if the weather craps out though.
A few tips to get the weight and bulk down and some gear suggestions -
Bring the lightest sleeping bag you own and sleep in all your clothing. It will also save you time in the morning getting ready to go.
Unless you tent to sleep cold, just bring the closed cell pad, skip the thermarest.
for clothing - my preference is to do baselayer, softshell top & bottom, lightweight puffy and a rain jacket (mostly to block wind) - watch the weather forecast and decide if you really need the heavier puffy. Extra socks are well worth the weight. Bring a THIN hat/balaclava (Ibex, smartwool, or capeline) you can wear under your helmet.
I would leave the ski goggles, they are just likely to fog up anyway. I would leave behind the overgloves.
You can cut the crevasse rescue gear down some, but I don't see any prusik setup in there. You can get by without a snowshovel, but it does make digging tent platforms a lot quicker. I usually do without myself.
Be sure to take fresh batteries, and possibly a spare set for the headlamp.
Personally would leave behind the deodorant, but bring hand sanitizer. Many people who get sick in the mountains do so from contamination on their hands not giardia, crypto, ect. Be sure to bring TP. Bring the highest SPF sunscreen you can find, and make sure it is less than a year old. You won't need the aquamira as all of your water will come from snow melting.
I would leave bottle cozie behind as well.
As for packs, if you work with your partner you may be able to have them carry the bulkier items so that you can get everything into the 54L pack, but for Rainer, something in between usually works better. If you do wind up with the 85L pack at least it will be easy to pack.
Have a great trip, hopefully the weather will cooperate, June can go almost any way weather wise on Rainier. The Emmons is a beautiful route, enjoy!