I started with plane group packings of heptagons.  The heptagons are not precisely regular as I used a simple construction method. That is I placed points on a unit circle with the angle difference of 2*pi/7.

For every space group 100 experiments were performed with random initial configurations.  The way the algorithm works now is that it doesn’t need feasible initial configuration.

The best know packing of heptagons is 0.892690686126509 which is also believed to be optimal. Same double lattice packing as withe pentagons.  https://blogs.ams.org/visualinsight/2014/11/15/packing-regular-heptagons/

Plane group: p2

Max density:  0.892607642589804

Mean density:  0.8425

Density variance:  0.0015

Number of infeasible solutions: 0

0.4777
0.2507
0.8900
1.9010
3.7421
1.0389

Plane group: cm

Max density:  0.8414

Mean density:  0.7251

Density variance: 0.0033

Number of infeasible solutions: 0

Plane group: p2mm

Max density:  0.7365

Mean density:  0.5760

Density variance: 0.0125

Number of infeasible solutions: 0

Plane group: p2mg

Max density:  0.8238

Mean density:  0.6826

Density variance:  0.0097

Number of infeasible solutions: 0

Plane group: p2gg

Max density:  0.892690618215488

Mean density:  0.8643

Density variance:  6.5725e-04

Number of infeasible solutions: 0

Plane group: c2mm

Max density:  0.7390

Mean density:  0.5719

Density variance: 0.0040

Number of infeasible solutions: 0

Plane group: p3m1

Max density:  0.5718

Mean density:  0.5377

Density variance: 0.0022

Number of infeasible solutions: 0

0.3232
0.3333
4.4878
5.7579