Advice with my Crazy Lager

I wanted to bottle my first lager yesterday but when I pulled it from the fridge and prepped everything for bottling, I noticed that fermentation had resumed.

So back story:
recipe: 1lb carapils, 4lbs of extra light DME, 2lbs of pilsener LME, hops, and Budvar Lager yeast (WYEast #2000)

Timeline: fermented at 54F for 4 weeks (until gravity went from 1.05 to 1.02), did a 62F diacytel break for 3 days, and then ramped temp down by 2F every day until I got to 34F. Let beer lager for 4 weeks at 34F.

Pulled gravity sample yesterday: 1.005 (temperature adjusted, triple checked reading this is all legit and measured correctly)

Meanwhile back in my brew room:

The carboy looks like it has champagne in it, the airlock is bubbling once per second.

My initial suspicions:
1) The beer needs to ferment more -- although how much further can it go down from 1.005?
2) At 34F there are a lot of dissolved gases in the beer which are becoming more insoluble as temperature increases -- the beer is not fermenting, but any dissolved CO2 is coming out (Henry's law)

My questions:
- do I let the lager sit at room temperature and then bottle, regardless of activity?
- do I put the beer back in the lager fridge?
- should I bottle now, and adjust my carb sugar to the low end?
- generally, what is going on?

This is my first lager and have almost 10 weeks invested in it, and don't want to mess it up.

Thanks in advance for all your useful feedback and constructive criticism.

Bringing the beer from cold to a warmer place causes a lot of co2 to expand and bubble out the airlock, so if the SG is unchanging you can bottle. Ignore bubbling.

Bottle with the usual amount of priming sugar. I use 1 oz of corn sugar per finished gallon of beer for most of my lagers.

Liquids and gas expand as they warm and CO2 comes out of solution as the beer warms. I'd bet your fermentation was complete before you started lagering.

Just to nitpick something: yes gasses expand when heated, but that is not what makes them come out of solution. Solubility is changed, which is different.

Really do appreciate the quick and helpful advice. Will bottle my beer today!