Two main problems I would have with it.
1. The numbers on the whole are a little too high. Some teams are losing money on sub-30 million payrolls, making them spend up to $35 million might not be fair. Lower the floor a couple million. Starting the luxury tax at $45 million is also a little high, the average team salary right now is under that and having it that high could still allow teams to "overspend" in certain situations. In my mind, the luxury tax should be at the average team salary for last year, which was I believe $41.6 million. Luxury tax should start at around that.
2. A luxury tax does not work unless there is a limit at which teams are stopped outright. A luxury tax is great in theory, but it results in two major problems. a) big markets continue to spend despite paying the tax, their fiscal advantage remains it just stings them a little more to spend a lot. If you don't stop some owners at a certain point, it is proven that some will keep going. MLB has this problem with the Yankees. And b) if or when some of the big markets spend despite paying the tax, the luxury tax system itself becomes inflationary and has the exact opposite effect of what you want it to do. This is another problem MLB has had. If too much is kicked back, small market teams increase spending and over time, theoretically, even the teams who don't want to pay the tax will be able to spend up to it.
Place a hard cap beyond your luxury tax threshold and your system could work.