Thanks for the questions; hope this helps.
No oil needed in the pivots while you are doing the pairwise check. I clean (wash) the movement in white spirit/paraffin or a proprietary equivalent anyway so at some level, the bearing surfaces ar ever so slightly 'oily'. I guess if you use water-based cleaning or re-finishing solution and the movement is degreased, yes, maybe a bit of oil on the pivots would not go amiss. without going off at a tangent (PTP), probably what happens is clocks are sometimes chemically etched or re-finished and therefore the brass working surfaces lose their burnished surfaces. Because the clock lacks power or doesn't run, bushing seems like the obvious route. If your clocks are ver squeaking (lifting pieces etc) that should stand as a major warning signal.
As part of checking the depthing, I would have checked for end-shake and side shake already, so hopefully, no problem there. I am highly suspicious of any clock that has been extensively bushed so look at the inside of the pivot holes for 'picking-up' and de-burr with 0000 grade steel wool. Like all clock repairers I look for 'silly' things like pins that are too long, the canon wheel touching on the inside of the hour why bridge if the friction spring isn't compressed enough. Bent pivots, bent teeth. For example when working on a French clock, I always roll the two barrels together. This immediately highlights bent teeth (much more likely on barrels). I am not a massive fan of testing movements on a test stand. I much prefer to completely assemble including dial and hands straight away unless I suspect there will be a problem. Could go on as fault finding quite a process. Happy to expand though if there is a particular area you want me to discuss. Basically, I do like most people do, wash the clock, check the depthing, check the mobiles drop freely from shoulder to shoulder when turning when the frame is inverted. Anything you think might not quite be right investigate and eliminate immediately. It almost never goes away. Anything like a recently replaced mainspring I am extra cautious of. Many times I've seen a new spring that is too strong or fractionally too high and rubs on the inside of the barrel cap robbing power. Sorry, could go on...
Yes re apparent wear. Controversial but pivots moving around in pivot holes, worn pinions and worn looking wheels are only indicators of possible issues. Personally I just shrug my shoulders at ovalised pivot holes unless there is an actual tangible depthing issue. There are exceptions of course and I do get that bushing is a rite of passage and is very much seen as doing a 'proper' job. I am very lucky not to have to respond (much) to peer pressure so it washes over most of the time but I am I admit in an incredibly privileged position.
The important point here (I think and may be wrong) is change. Most folk regard clocks as part of material culture and a record of something. Nobody quite knows what that record means or what we quite do with it but we feel it is important. I would agree with that. With plenty notable mistakes and blunders and irreversible damage I have caused, I try and stick to the there conservation tenets of minimum intervention, reversibility and accountability. At the risk of sounding pompous and/or conceited, these broad guidelines make me ask "really?", "is that right?" and so-on.
I know people are understandably after practical advice, but ultimately it is the thinking and questioning that I feel is important. Inevitably the interventions I carry out today, I will look back on with horror. Things change... which is good.
The only other wear test I have seen is to try the mobiles in a depthing tool. Personally, for the vast majority of clocks, I find testing the mobiles in pairs takes only a minute or two per train. If something doesn't feel right that cannot be explained by re-depthing and bushing, then a closer inspection in the depthing tool is the next step. It would be really useful if there were other way of testing the 'health' of a train. I think I mentioned it already but a Microset timer can be a great diagnostic tool for clocks with anchor recoil escapement because you can use escapement error as an indicator of cyclical amounts of energy at the escape wheel.
Try it.
Hope this helps. Sorry it is a bit of a rant. Hopefully it doesn't send people into a rage. I see loads of bushing without depthing. Remember also the conjectured "original" centre is only an indicator. We cannot ever put the mobile "back" as it once was.
Lots more to say if anyone wants it...
Thanks again for asking...