I have the original Standard 10 rear axle in my '62. It has a limited slip differential and Standard axles. I run 185-70x13 RA-1s on 6" wide rims with an 85Hp 109E (1340cc) and the 3-rail close-ratio gearbox. The differential housing has been reinforced back in the mid '60s and has held up very well for me so far.
I bought a pair of axles from Chris Beebe back around 2010 when I rebuilt the suspension on the car. I put new wheel bearings and seals in at that time. I replaced the axles because they were wearing and couldn't hold sufficient press fit (in my opinion) to the wheel bearings.
Bear in mind that if you change to the Cortina/Escort rear axle, the wheel bolt pattern is different than the Standard / Triumph pattern that you have now. The Ford axle has a 4x4.25 bolt circle while the Standard/Triumph has a 4x3.75" pattern. So you will incur additional cost in one of the following forms:
1) A new pair of rims for the rear wheels if you don't mind having two different wheel bolt patterns.
2) A set of adapters for the rear axle if you wish to keep your present wheels.
3) A pair of new hubs for the front spindles and a new set of four wheels if you want to use the Ford bolt pattern all around.
Or as you have already noted, you can go with the TR-7 rear axle set up. It has the advantage of having the same 4x3.75" bolt pattern as the Standard rear axle. So you would only be into it for the cost of the width modification.
Also please note that for replacement axles for the Standard unit, I have heard that the TR-7 axles can be shortened and re-splined at the inboard end to fit.
Another option you might consider is the BLMC Midget/Sprite unit (4x4" bolt circle). these are also sometimes fitted to Sevens. There are limited slip differentials available for these axles. Here is a comparison of the Spridget unit to the Standard out of my car:
Another option to consider is the Datsun LB110/210 (1200 / B210) unit. it has the same bolt pattern was the Ford axle.
The other option that I have looked at is the rear axle from the 1st generation RX7. In late production GSL trim they were fitted with disc brakes. These also have the Ford bolt pattern.
As for the S10 axle, I wouldn't think that is a very good option. Besides the Chevy 5-bolt pattern axles I would guess that the axle assembly itself would be much heavier. If so, that additional unsprung weight would dramatically upset the spring / shock balance of the suspension. Not to mention the overall mass balance of the car.
Just my $0.02.