Eames Lounge Chair shockmount failure - alternatives?  

Like trying to reinvent the wheel
I believe the intent was to have some "give" engineered into these chairs,therefore the L bracket would go against what the original concept was;a comfortable chair with some flex.

Not
that they do flex to any useful (comfort improving) amount. I would trade this very flawed design in on any of a number of other more comfortable and better structurally designed lounge chairs.

Better than a nut and bolt
I'm thinking that a L bracket would allow some 'give', at least more so than inserting a nut and bolt into the shockmount area.
When working properly, the shockmounts does provide enough 'give' to make the chair quite comfortable.
My chair's first shockmounts came apart after 3 years, and the second set (fixed by Herman Miller), after a further 12 months.
There is something seriously flawed about the design.

Your mileage may vary.
My early '70's 670 received its first set of 4 replacement shock mounts by HM sometime prior to 1995. I bought the chair in '03 and have since reglued one of the replacements to the seat pan in '05. The chair gets daily use by teenagers who, despite repeated admonishments, treat the chair as teenagers will. Currently, the chair displays no signs of imminent failure, though I do make frequent inspections.
Environment may play a role in premature failure, but I think repeated dramatic swings in conditions would be worse than a relatively stable warm, high-humidity situation.
A 12-month life for an OEM repair would warrant negotiation with HM, IMO.

What's your goal?
Are you trying to prevent the shockmount failure, or do you just want to prevent catastrophic damage to the back when the shockmount fails?
I don't own a 670, but from what I remember about the ones I've seen, there's space in the shockmount area to mount a short cable between the arms and back -- long enough to allow the back to flex freely, but short enough that in the event of a shockmount failure it would arrest the backward movement of the failed side before the other side snapped.