When taking DOPE, what's the acceptable delta between Density Altitude values before I have to take new DOPE? Concurrently, what's the acceptable delta between range to target before I take new DOPE?

It depends of course on your target size, distance, and other factors, but a general consensus in long range hunting circles is that 2,000 ft DA increments are as fine as you need to go. Some say 3,000 ft is adequate. Playing with a ballistic calculator will show you that these increments add up to only a click or two (if we're talking 0.1 MIL clicks) for a lot of cartridges inside 1,000 yards.

The most effective way to implement this, that I've seen or used, is to make up dope cards in 2,000 (or 3,000) ft increments, starting with the lowest I expect to use. In my area that'd be -2,000 ft, going up through zero all the way to 8,000 ft to cover both summer and winter here in the mountains of the pacific northwest. That's 5 dope cards, but realistically in any one trip you'd only need to bring 3 of them. If you laminate the most frequently used card on your rifle stock (say, the 2,000 ft card for example), you could carry two others laminated back to back on a single card for reference.

Hope that helps!