I'd recommend not storing an alcohol stove inside cookware, because denatured spirits are often crossed with methanol to make them unfit for drinking. methanol is posionous even in microdosages with a common non fatal result being temporary or permanant blindness as well as death.

yes, tarp tents, down, and alcohol fuel stoves is the way to go for ultralight bike camping.

silicone coated microweight nylon and epic non coated waterproof tent fabrics can give you tents that pask up impressively small. Bibler's parent company, Black Diamond, makes some of the bibler tent models in ultraweight Epic fabrics, some models pack up the size of a one liter water bottle and when pitched have amazing inside space! I'm using a Black Diamond Lighthouse, 3 pound, 4 ounces or so. big enought for two and room to sit up and even kneel without bending over.

my silicone Golite Hex tent (like the OP's Mountain Hardware KIVA) packs up at 1 pound, six ounces without the pole or stakes and is as small as a grapefruit when packed in a compression sack. let me say that again -

The Golite HEX tent can fit you with your bike inside, and packs down to the size of a grapefruit.