Since the root cause of what you are trying to address is the reward having, I'd suggest considering an adjustment to the having schedule. Instead of their being a large supply shock every four years, perhaps the reward could drop every 52,500 blocks (yearly), or even at each difficulty adjustment, in such a way that the inflation curve is smoothed out. The exponential decay rate would be preserved, so overall economic philosophy would be preserved.
I'm guessing hesitance to this approach would lie in a reluctance to tinker with Bitcoin's 'economic contract', and slippery slope concerns about might be the next change (21M?). However, I think it could actually increase confidence in the system if the community is able to demonstrate a good process for making such decisions, and show that we can separate the meaningful underlying principles, such as the coin limit and overall inflation rate, from what is more akin to an implementation detail, as I consider the large-step reward reduction to be.
I'm not too worried about the impact of the having as is, but adjusting the economic parameter would be a safer and simpler way to address the concerns than to tinker with the difficulty targeting mechanism, which is at the heart of Bitcoin's security