How are you heating sparge water? Can you batch sparge?
If so, collect enough from the mash for your old ale, then add enough 170F sparge water for your mild's gravity/volume. Seal up your mash tun and wrap it in a blanket until you've finished up the first boil, then collect the second runnings.
Your mash tun will hold temperature much more consistently than another kettle or bucket.
If you're heating sparge water in your kettle and no-sparging, just wait until after you've finished your first boil to sparge. The sealed/wrapped mash tun should keep the grainbed temp fairly consistent, and the low amount of water in the bed will minimize enzymatic action during the wait time.
Hope this helps. I did this a few times when I had smaller equipment. It makes for a long day, but its no big deal, especially if you start early!