You will be aware of the difficulties of setting hypoid gears from your own experience and reading the various issues on these threads. Most probably (and wisely) you will be extremely careful from whom you take advice on setting hypoid gears.
Considering my last sentence I had best tell you of my own experience before proffering any advice. Up until 3 years ago I was rebuilding R-R and Bentley axles, with a few from Alvis and Aston Martin, this after a first Worldwide career in Automotive and Plant Engineering including Military gears. That is the shortened version, and on R-R post war six cylinder cars alone I rebuilt some 630 off hypoid axles in secondary retirement. You might appreciate that those units have to be super quiet and therefore deadly accurate.
Firstly you are running into a problem experienced by owners completing axle work and may I say a large number of rebuilders and specialists. The main problem here is misunderstanding of how hypoid gears are made, more later.
I would like to offer an analogy, and ask two questions of you, to illustrate your problem. If you were to contemplate using second-hand exhaust valves in your engine say because new ones were not available…….
(1) Would you take those valves and fit them in your engine as received, or would you attempt to reface and lap the valves? I would guess you would most certainly lap them into the valve seats.
(2) Why would you not therefore ensure the second hand crown wheel and pinion were also lapped together before use?
Your Crown Wheel and Pinion will have been running together with worn bearings and at best in different axle case positions, trying to match them without first lapping is a pointless exercise.
The gears you have were cut on a Gleason gear cutter and need lapping on a Gleason lapping machine, (probably cost about £120). Any gear company will then stamp the pinion with the new setting dimension, say for example, **2.625 inch. After making sure the pinion bearings are pre-loaded, (even temporary) the pinion will need shimming to achieve this **dimension. That measurement is between the raised facing on the pinion and the differential centre line. The Crown Wheel will then require positioning to achieve the required backlash figure.
Notice, no marking paste has been used, and neither was paste used on initial production, all that happened was that the operator replicated the gear cutters setting. Do you really think that a manufacture is going to paste up gears coming down a production track every two minutes, or are they going to use the gear cutting measurement? In small scale up market production, paste would be used, along with the Mark 1 Ear to finalise noise abatement setting and that exercise was carried out on a lapper. For my own part I have used paste only twice and that to quickly prove Crown Wheels that were “dished” during hardening.
.Pasting gear sets in cars originated with Bevel and Spiral Bevel gears when garages were little more than blacksmiths and had very little tooling. It was an easy way to match slow moving gears. Motoring technical illustrators embraced the method and the same type of illustrations continued to be published in motoring journals from the conception of hypoid gears long after more accurate methods could be employed. It is often easy to see that an illustrator has copied the text and sketches from years ago and sometimes even mixed bevel gearing with hypoid gears.
Earlier I mentioned the way Hypoid gears are made. Ask most owners just how they think the gears are produced, the likely answer will be by turning or grinding but nothing more will be forthcoming. In fact, after rough shaping the Crown Wheel for instance is rotated against a rotating set of chopping blades. After each cut the unit is advanced about 0.0006 inch and another cut taken. This method leaves a set of extremely fine flats on the gear surface that can be eliminated by lapping or operating the gears for a few thousand miles. Once gears are run out of line, (and that starts to happen immediately the gears are run under load), similar wear flats will occur, and they need eliminating to prevent gear noise.
You have not mentioned the CW&P ratio, apparently you are using the S Type and E Type axles but these had numerous ratio’s as did the gearboxes. If you are using a fully synchromesh gearbox , standard radial tyres and 3.4 engine I think you will find the 3.3:1 ratio useful.