A longer time period over which the reward is given doesn't help, as the larger nodes or entities will still get a larger ratio of the rolling over fees, by definition.
While writing a response to this, I realized the situation is actually much more nuanced than I thought.
Big miners don't have an advantage over small miners. Rather, the existence of big miners shifts the balance of the system as a whole, creating a situation where miners get more rewards, users pay less fees and/or get more of their transactions included, while nodes have to deal with larger blocks.
Here are example scenarios, with made up values for the penalty function. I assume for simplicity (not a necessary assumption) that there is endless demand for transactions paying 1mBTC fee, that typical blocks are around 2K txs, and that there are no minted coins. The pool clears at 1% per block.
Scenario 1: The network has 100 1% miners.
Every 1% miner knows he's not going to claim much of any penalty he pays, so he includes a number of transactions that maximize fees-penalty for the block. This happens to be 2K txs, with a total fee of 2 BTC and penalty of 1 BTC.
The equilibrium for the pool size is 100 BTC.
Miners get 2 BTC per block (2 fees + 1 pool collection - 1 penalty).
There are 2K txs per block.
Scenario 2: The network has 1 90% miner, and 10 1% miners.
The 1% miners build blocks with 2K txs, fee 2 BTC, penalty 1 BTC, like before.
The 90% miner knows that if he includes more txs, he'll be able to reclaim most of the penalty, so the marginal effective penalty exceeds the marginal fee only with larger blocks - say, which have 4K txs, 4 BTC fees, 4 BTC penalty.
The average penalty per block is 3.7 BTC. The equilibrium pool size is 370 BTC.
There are on average 3.8K txs per block.
A 1% miner gets, per block he finds, (2 + 3.7 - 1) = 4.7 BTC - more than in scenario 1!
The 90% miner gets, per block he finds, (4 + 3.7 - 4) = 3.7 BTC - less than small miners get in this scenario, but more than miners get in scenario 1!
To restate what goes on - the big miners create supersized blocks because it benefits them, but it benefits the small miners even more.
Miners are happy. Users are happy. Nodes are not happy.
But note the following: Big miners make the mining rewards bigger, but you don't have to be a big miner to enjoy it (small miners actually are at an advantage). So if a miner becomes big, he encourages more people to start mining, raising the difficulty and countering the effect.
So more analysis is still in order, but overall, I don't think these dynamics encourage the formation of big miners.