The problem turned out to be the O-ring plug in front of the sump screen. The sealing surface upon which the O-ring seated was scuffed. Roll to inverted and the oil pressure recovers in 2 seconds.
Oil pressure is maintained on the vertical line.
As can be expected I received many good suggestions, some of which were not relevant to my problem, but as they are certain to be relevant to someone else in the future they are included. I have an Pitts S1E with the standard Christen Inverted Oil System. At the same time the inverted oil system was cleaned and overhauled, being reinstalled with new hoses everywhere. Everything is back together again and flying, but the oil system has problems. You didn't say whether you have a constant speed prop or a fixed pith prop.