You asked, "Does the fact that it is constitutionally limited require the government to offload public property at a loss, or at below market value?"
No, that would make no sense - and I did not call for that at all. I said sell at auction - meaning at market value. And before that I said, "at best possible price."
You asked, "If the government holds land which cannot be sold at a reasonable value but which can be managed, say, as grazing land, by a private agency which bids to pay the treasury for that right, until such time as the land can be sold for a good return, is this somehow a violation of my rights? Of yours?"
In your hypothetical you speak of holding the land temporarily to wait for a better price and this implies the principle I discuss - get rid of the land not needed for protection of individual rights and at the best price.
You go on and hypothesize about the government being in the land rental business in general, the grazing rights business in particular - this is not good because it is a form of either unfair, or incompetent competition with other land owners - the government should not be in the banking business, the auto manufacturing business, or the livestock grazing business. Yes, that is a violation of our rights.
You said, "There is no right to force the government to offload public land which is not a drain on the treasury simply because the mere notion offends absolutists. Selling public land at a loss would be the only real crime."
First, I'd mention that it is a better perspective to say that the constitution doesn't grant the government the right to compete with private land owners. We don't need a 'right' to force them to do what they shouldn't be doing in the first place.
Asking the government not be in various businesses, like land rental or insurance or mortgage is not being "absolutist" - it is being consistent with free market principles and recognizing that government may not do what it isn't constitutionally authorized to do.
I'm not advocating selling at a loss, whatever that means... just sell it for the best price obtainable over a reasonable period of time. There may well be more public land (particularly in the West) than there is privately owned land. This causes major distortions in the markets that are directly related to land. We are all paying for this - and as to it not being a drain on the treasury - that's a crock. The inept and expensive management of public lands (BLM, Fed. Wildlife reserves, National parks, National Forest Lands, National monuments, etc., etc., etc.) is expensive and there is a very real hidden cost of the land not being available for private use driving up costs in many area and distorting markets. Obama proposed about 10 million acres to the federal lands that are locked up as national monuments by executive order. The Fed controls about 650 million acres already. Bush grabbed control of 200,000 square miles of ocean with executive order making it an undersea park or some such. When you see over 60% of some of the western states owned by the government, I'd say it is a major issue and not just about waiting for a better price.