I've been tarping it in Washington for the past dozen years, and generally I've found it's easier to stay dry with an adequate tarp than with a tent with a built-in floor. The "bucket floor" doesn't just keep water out, it has annoying tendency to keep water in. Combined with the condensation issues in a lot of tents on humid, calm nights and well....
Make sure your tarp is big enough, covering significantly more ground than your ground sheet. Try to pitch it in a place that will not turn into a puddle (hint: water flows down hill). Pitch the tarp and put all of your gear under it, still packed up in waterproof bags. Get under the tarp out of the rain, take off wet rain gear and shoes, than un-pack your dry gear.
You have lots of ventilation and a dirt floor, so go ahead and cook under there. Try not to go out from under the tarp more often than needed in camp, each time you have to fight to not bring water in and get it on your sleeping bag and such. If you are going in or out after your sleeping system is set up, than fold your bed in half, with it's ground sheet, like a big sandwich with waterproof stuff on the outside. Than you can mess around with wet things (rain-gear, wet pack, etc.) without getting water in your bedding.
If you do get stuck camping somewhere that doesn't drain, do like a previous poster mentioned and prop up the sides of your groundsheet with things. Using a bivy or sleeping bag cover can make this process somewhat easier.
Note, if you use your pack as part of your ground insulation and it's sopping wet from hiking in the rain, just put it down underneath your groundsheet or bivy. Try not to bring wet stuff into your dry world you've created, and carefully manage your transitions from dry to wet.