Would it be possible to create a soft-fork for reducing miner reward?
Yes, it is possible. The rule regarding the coinbase reward is that a miner cannot take more than the block subsidy plus the transaction fees in the block. This means that a miner can opt to take less than the full reward that they are entitled to. This has happened before in Bitcoin a few times. The coins that they did not collect are gone forever.

So, you can use this rule to your advantage if you want to decrease the block subsidy via a soft fork. In your soft fork, you simply create a new rule which results in the coinbase reward being less than the current coinbase reward (e.g. the block subsidy is smaller). Because of the rule mentioned earlier, non-upgraded nodes will still accept blocks that have these coinbase transactions with a smaller coinbase reward. Thus this is a soft fork because the new rule is backwards compatible.