1) Burn a part of the transaction fees and distribute them later (e.g. in the next halving period) in the form of a tail emission. This means that the supply will not be touched at all.
Imagine that your employer says to you, "In order to motivate you, we are going to hold half of your salary for 4 years."
2) Create a second official Bitcoin token which is distributed in an infinite manner, e.g. 1 per block, to miners, from a specific block on.
This will only work if the token retains value. First, I don't see why it would hold any more value than any other alt-coin. Second, an inflationary coin will eventually see its value drop to 0.
Also, if the coin does somehow retain value, then it would be competing with Bitcoin.