I like the direction, but for me I'd tinker a bit.
The Support Level II is great, but do you really want to commit a full third of your force to static roles? And you don't really need to give your motorised infantry TAG, because they shouldn't be that far ahead. Better off pushing your TAG into the recon groups.
The recon groups - pity the Tufana is a post-Jihad design. It's a lovely scout. Maybe the 3058 Pegaus with BAP & TAG would be a good replacement. I'd consider replacing the Drillsons with fast 'Mechs - Buccaneers (5W) and/or Raijin (200-C).
The first battle group is a little light - I'd almost call them a recon group, not a battle group. They're very flexible though, so I wouldn't touch them, just rename them. The second battle group is your brute squad, with the Galleons giving them flexibility.
So maybe:
- 1 support level II as shown
- 2 Pegasus/'Mech recon level II
- 1 Chevalier+Bolla general purpose Level II
- Brute Squad level II as shown
- and to round it off I'd probably go for a heavy Level II - a couple of Pumas, an Excalibur (RAC version), Grim Reaper, and a generic omni off the IS list - maybe Avatar - for a Level I of Purifiers to ride on.
But that's my slant. Your proposed Level II is a darned good plug, or dam wall, to hold an objective against pretty much anything.