It is difficult using positive TSR as a way of justifying higher...

It is difficult using positive TSR as a way of justifying higher earnings multiples, because it can be achieved without any change in earnings. If profits remain flat and the share price doubles can we say the higher PE is justified because my return was 100%?

PE's are forward looking indicators. A higher PE may be justifiable if earnings are expected to accelerate, or become more predictable, or interest rates or tax changes are going to affect the valuation method for example. If some of these factors don't exist then the PE might have moved up based on price speculation only and this might be a poor indicator for future shareholder returns.

CSL and SNL have certainly had earnings rises over the time frames you have chosen. Accordingly share prices should also have increased (even with a steady PE). For PE's to rise over the same time frame the share price growth will have outpaced the earnings growth and for this to occur we will need to assume the earnings growth outlook is brighter than the past.