As more ASICs hash away for acceptable difficulty, the difficulty keeps rising over time. Greater difficulty means to me that more electricity is used to secure the Bitcoin blockchain. Are there clever ways to modify Proof of Work, continue to use existing ASICs, spread block extraction to more miners, and continue to secure the blockchain without increasing power requirements? I'm not interested in other algorithms like Proof of Stake, Proof of Burn, etc.
No, because by design PoW is assigning relevance proportional to power usage.
If the market pays N USD per day worth of BTC to miners (in subsidy + fees combined), then the mining ecosystem will converge towards spending N USD minus profit margins. Not all of those costs go to electricity (as there are also employment and hardware costs from failure and depreciation), but a significant fraction of the costs do go to power.
It is absolutely irrelevant what the actual PoW function is, from this perspective.
The security of the Bitcoin network is dependant on the financial incentives built into mining. This means that the amount of energy used to secure the network is not really important, it is the cost of that energy that is important! To make this more obvious, think about what you would need to consider when planning to majority-attack the network: how much will the attack cost? The availability and cost of electricity will weigh into this consideration, but ultimately the cost of the attack vs the expected return is what will really matter.
For another perspective on this, consider a futuristic civilization that has developed highly efficient energy capture and storage, driving the price of energy ($/kwh) down extremely far (eg 1/100 of today's prices). Compared to today's network, such a civilization could use 10x the energy mining, while having less effective security! This is because the dollar value of the security is lower:
(10x energy)*(1/100 price per energy) = 1/10 the $ value! An attacker would only have to spend 1/10th as much money to attack the network - this is less secure, by definition.
As Pieter mentioned, there are costs to mining beyond electricity, so perhaps by reducing these external costs a miner could provide 'more security per dollar spent', but notice the important measure is still 'per dollar spent', not 'per kilowatt-hour consumed'.