If they are Neutral than they make mechs for Katherine until the 7th Crucis arrives and with a superior Davion force on planet they then switch to producing mechs for Victor. Either before or during the 7th Crucis' occupation the Highlanders set out on their series of raids against the Jade Falcons. Not wanting to jeopardize their neutrality the Highlanders sit out the fighting for Inarcs and the factories. Given that at the time the factories are damaged the Highlanders are probably still recovering from their losses on Twycross they are probably at less than 2 companies in strength.
While it isn't mentioned how large a force seized Inarcs by the first battle only a single 'Mech battalion from the Seventh Crucis supported by two armor battalions and the 405th Federation Interceptor Wing was stationed on Inarcs. By the second battle, only two reinforced companies of 'Mechs and a single battalion of armor remained (no mention of aerospace support).
If they are neutral removing themselves from the conflict is the best option. Yes the factories are damaged in the fighting but that cant be helped since their neutrality is far more important to Blackstone then protecting their assets. In one scenario the family/corporation looses a year or two of production, in another they loose their rights to their business all-together.
It is implied that the damage to the factories was caused by sabotage rather than combat damage ("the six-week delay had given the Lancers time to cripple the Blackstone Industries plants", FCCW, p148).
If they are pro-Katherine things get trickier. My best scenario is that they were raiding the Jade Falcon territories when the 7th Crucis struck and during the 9th Lyran Regulars counter attack. This would put them out of communications with Inarcs for the duration of their raiding campaign. They only return to the planet in 3065 as either an auxiliary to the Neerabup MTM or after the fighting is over. It should be remembered that by this point they are probably close to 2 companies in strength and would be easy to omit from the record. From here they spend the rest of the war recuperating.
Possible. Unfortunately, MSU states that the Blackstone Highlanders spent "four years of relative peace, broken only by the occasional pirate raid, enabled them to rebuild to full battalion strength with ease." While they might have spent part of those four years on Inarcs after the survivors from the Seventh surrendered where did they spent the other two years? The BH rely on Blackstone Industries for most of their income not to mention new machines/parts and with the FCCW raging on it would be a seller's market with most new production already sold to one of the participating factions so rebuilding without direct access to BI's factories would not be easy.
So where were they? Arc-Royal? While a relatively new mercenary world, they would likely have difficulties acquiring new machines and they certainly wouldn't engage any pirate raiders (assuming any were foolish enough to attack the homeworld of the Kell Hounds and Clan Wolf-in-Exile one or the other would handle raiders). Same goes for Outreach. Galatea? For most of the first half of the FCCW Galatea was in chaos with various factions forming, fighting amongst themselves, breaking apart and forming new factions. Not a world one would go to to rebuild.