I am trying to motivate me to do this project for months now, and I looked like nobody cared about it.
Thanks to Google webmaster tools (not Google Analytics, I care about your privacy, dear reader), I was able to see which other site linked my blog. Reddit does it! Woo-hoo!
https://www.reddit.com/r/FPGA/comments/34owkn/open_source_fpga/
pointfree refered to my blog in a comment. Thank you mysterious reader!
IceStorm project
In the same comment thread is also discussed about the IceStorm project [1], which aimed at reverse-engineering the bitstream format of the Lattice iCE40.

I even bought a stick to give a try! [2]
They managed to have the complete software chain open source: from verilog to bitstream. The stick features the iCE40HX-1k FPGA chip from Lattice (datasheet: [DS1040], digikey: [3] approx. 5€).
Is it interesting for dynamique partial reconfiguration?
According to [DS1040] (v3.1, p.3-17), in slave SPI mode, the maximum input clock is 25MHz (readback is 15MHz). The FPGA can be configured using SPI interface in ~25ms (with medium frequency SPI mode, 24MHz). The bitstream is 34112KB ([TN1248], p.11). Lattice does not seem to have developped any user-friendly way to use partial reconfiguration.
According to [TN1248], p.4, the SPI configuration flow requires a CRESET_B to restart the configuration sequence.

[TN1248], p.18:
After driving CRESET_B High or allowing it to float High, the AP must wait a minimum of 300 μs, allowing the iCE40 FPGA to clear its internal configuration memory.
Looking at [HB1011] and [DS1040], there does not seem to be any JTAG interface in this chip family.
Conclusion
Partial reconfiguration seems impossible with the iCE40 FPGA.
References
[1] | Clifford Wolf and Mathias Lasser, Project IceStorm, http://www.clifford.at/icestorm/ |
[2] | Lattice Semi., iCEstick Evaluation Kit, http://www.latticesemi.com/icestick |
[DS1040] | (1, 2, 3) Lattice Semi., iCE40™ LP/HX Family Data Sheet, http://www.latticesemi.com/~/media/LatticeSemi/Documents/DataSheets/iCE/iCE40LPHXFamilyDataSheet.pdf |
[3] | Digikey, Lattice Semiconductor Corporation ICE40HX1K-TQ144, http://www.digikey.de/product-detail/en/ICE40HX1K-TQ144/220-1565-ND/3083575 |
[TN1248] | (1, 2, 3) Lattice Semi, iCE40™ Programming and Configuration, http://www.latticesemi.com/~/media/LatticeSemi/Documents/ApplicationNotes/IK/iCE40ProgrammingandConfiguration.pdf?document_id=46502 |
[HB1011] | Lattice Semi, iCE40™ LP/HX/LM Family Handbook, http://www.mouser.com/ds/2/225/iCE40FamilyHandbook-311139.pdf |