I was a dealer with an inventory well above that number. I agree, pricing each car individually is tough with today's technology options. However there are pricing rules in a number of inventory management solutions out there that makes things a bit easier. I used to do this for a new car auction solution and it took a few hours of work each month. I do see things improving in this area soon 
Along with having that 1,000+ new car inventory most of the manufacturers (Honda being one of them) I worked with did not want you to advertise below invoice.
Right now, most car dealers show MSRP for the exact reasons you and I both stated. Being the first dealer in the market to do different is rewarding. I know; I did it. It scared the crap out of our GM's and sales managers, but when I could talk them into it we had customers in the showroom within hours of the changes publishing.
If you do go down the new car pricing route you will have to get aggressive at some point. How many sticker deals are still happening on Corolla's, Civic's, Focus' and the other volume models? If you know and track your PVR per model/trim then you have the intelligence to price your cars accordingly. The real trick is retraining your staff to operate in the modern world.
Profit makes the world go 'round. There are ways to maintain and/or increase profit and those ways are being taught to us whether we like it or not. Phrases like "risk of 'short-selling'" and "negotiation is a part of the business that will never die" translates to "I'm afraid of change." I don't think you're really saying that Matt, but I do think you should step outside the dealership for some new perspective. I need to find a way to help show the new perspective I have after 20+ years in the dealership vs. 9 months out of it. It really is amazing. I just haven't formulated the words yet.
Maybe there is a middle ground that will be determined by the car dealer. I doubt it though. I hate to say that, and I hate to say that because it is knock against my family (who owns and operates the dealer group I come from). I'm getting an education on the vendor-side of the aisle right now and I'm seeing how the OEM's are viewing the future. They're more consumer-minded than the typical dealer. I also look at history and know that in a capitalist society the consumer determines the market.
There is definitely a struggle between the brick sales floor and the digital sales floor that is undeniable. I see it as the roots of change. It is coming; all outlooks point toward it.
A really basic timeline on technology changes toward pricing:
Internet >> wider invoice and trade data for consumers >> used car pricing & stocking (vAuto, First Look, AAX, etc) >> incentives feeds >> price quote tools (ResponseLogix) >> ________?
