I upgraded to MyHDL 0.10 and the new API. Browsing through the VHDL, it seems to have fixed this issue. No constants are defined in the VHDL file anymore. Instead, the computed values are now hardcoded into wherever they are used, and each instance gets its own set of values.
The upgrade caused an unrelated major nuisance, though: I get “ToVHDLWarning: Previously used name being reused” warnings every time I rerun the conversion. In simulation, the blocks are renamed on every run, so that it is necessary to manually add all signals in GTKWave every time I run the simulation. After the latest simulation, the blocks are named biquad0_0_1_2_3_4_5, biquad1_0_1_2_3_4_5, and biquad2_0_1_2_3_4_5. (I added this as another issue, but I mention it here as well, since the code is already in this thread.)