Then you'll have to mine your own blocks. Just as miners can't modify the block subsidy to give themselves double the reward, you also can't just rewrite the rules to take half the fees from them.
I think you overestimate the miners' power in the game. If the Bitcoin users and holders think that the version of Bitcoin is superior to the version without that burning, then there will be enough miners happy to mine the new protocol. And if they don't want to support a softfork you can threaten with a hard fork. The Bitcoin users have always the last word, as seen in 2017 
Anyway I don't understand why you think the miners wouldn't like the idea. It's them who will benefit in the end. If the transition to the new protocol is designed well, there will only be a short period where miners won't get coins from the "burnt coins pool". So the proportion of burnt coins could start on a minimal percentage of the fees and then increase over time. Also the delay before the coins are reinserted into circulation by another miner could start with a few blocks, and this delay could become longer each difficulty period until a stable state is reached after a year or so. Once this transitional period has ended, the income for miners will be typically higher than before and they have a predictable minimum income.
When large corporations have a significant stake in BTC, they'll want to support the network's security. Even the average user would likely be willing to contribute something to protect the value of their holdings if block rewards become too small to sustain the ecosystem. This kind of subsidy could be proportional to each person's holdings -- like paying a few dollars a year to keep your $10,000 safe. I don't think most people would object.
I think that's the same idea like @odolvlobo already mentioned about a demurrage. The problem with that may be the competition of altcoins which don't follow that path. Monero for example has already switched to a tail emission, so they don't need this "tax" ...