How about, claw can be used for an infinite amount of time, but can't actually make any attacks and guns can't be fired while using the claw. The point would be that you shoot yourself towards the mech you want to kill, grab ahold and then stick as many C8's as possible to it before they explode and kill you.
This way, BA still has a perfectly good reason to use the claw; sticking C8 to moving mechs as it is is very hard, and sticking 3 to the same component in a short period of time is near impossible. The claw would guarantee you about 3 C8 hits to the same place if you managed to attach, surely that's good enough?
It also forces BA to get off after attacking, sidestepping the problem of them just sitting there forever slowly stripping off armor without the mech being able to do anything about it. Of course they can still sit there forever but if they're not doing any damage, who cares? And you don't need any artificial gameplay mechanic like "oh the claw's run out of fuel".
Also BA could still use the claw to ride friendly mechs, which is another important use of it.