Tricky. If you can tolerate a voltage lower than 3.3V the MS412FE at 4.8mm x 1.2mm might do the trick:
http://www.sii.co.jp/en/me/files/2014/11/BAC3011EJ-01C1409_web__.pdfIf its charged to 3.3V you might, if you're lucky, get your 2 or 3 days with the voltage above 3V, and a lot longer >= 2.8V. Low temperatures will reduce the voltage though and charging to 3.3V will reduce the cell's life but the datasheet is not very helpful as to how much.
At 4.8mm, would that give you enough space to squeeze in a boost converter such as the TLV61225? Its 2.4mm x 2.15 x 1.1mm and needs an inductor; they also recommend 2 10uF caps but you might get away with the battery (and perhaps a small cap) on the input and you might already have enough capacitance on the o/p side?
If you haven't got space for a separate converter, could you toggle a spare pin on your CPU to drive a charge pump with a capacitor and 2 diodes to boost the voltage? Might be a bit tricky bootstrapping the micro out of a low power sleep mode though. And don't charge the cell above, say 2.7V so the o/p voltage doesn't get too high, depending on what voltage regulator(s) you have. Or add a zener diode after the charge pump if you have room.
Alternatively, could you use a different form factor? EnFilm (now owned by ST) make a .7mAh cell with nominal voltage 3.9V. Its 25.7mm x 25.7mm, but its only .2mm thick. Unfortunately I don't think you can fold them or roll them up!. They're also horribly expensive at $38 one-off from Digikey! See:
http://www.st.com/web/catalog/sense_power/FM142/CL848/SC1107/PF250531?icmp=pf250531_pron_nb_jun2014&sc=enfilm-nb