I'd take the average HR from the junction or from after the flat parts at Rock City to just below the final pitch and use that at LTHR. Visually estimating it looks like about 178.
I think that the final wall is not good for getting your max. You have spent too much time climbing by the time you get there and won't be fresh enoug to really go all out.
It's more accurate to set zones based on LTHR than max HR. The way the max HR zones are calculated is to apply a standard percentage to obtain an estimate of the LTHR and then the zones come from that. But the standard percentage, while based on studies, is only an average number for the people in the studies. While I don't think it is as inaccurate as 220-age, it's not all that accurate- your LT moves as you get fitter or less fit, while your max stays the same relative to fitness but decreases with age.