I think the sumps are slightly different between 1300 & 1600s but can't be dead sure as my parts books don't cover anything after 1975/76 - but also be aware that the Dipsticks & their guide tubes are different between 1300 & 1600s as well. Be aware that sump pans vary between Mk1 & Mk2 Escorts, and Cortinas. Before thinking about changing the sump pans over, check for a stamped part number on them somewhere - mine are greasy so don't ask me where - and compare the numbers.
Sounds to me like your main problem is with the starter motor - the Autos use a Bosch pre-engaged type of starter motor, same as those used on the 2 Litre Pintos. The Bosch starter fitted to all Escorts is shorter than the one fitted to Pintos in Cortinas, due to crossmember clearance issues on the Escorts. The flex plate from the auto also has a different diameter ring gear to the manual gearbox version, and the lead-in chamfers on the gear teeth are all on the opposite side to the manual ring gear. If you are using one of the Lucas inertia type starter motors, the pinion gear is also a larger diameter than the Bosch starter pinion, and will not be engaging properly due to this difference in Diameter and the fact that the Lucas starter needs the chamfered lead ins on the opposite side. The Lucas inertia starters are only factory fitted to manual gearbox 1300 & 1600 Kent engines.
That screeching sound you mention sounds like the Starter Motor Pinion gear to me - it isn't disengaging from the Ring Gear and is also likely rubbing against it. I had a similar problem when my Lucas Starter (they're not the best design) had the pinion gear stick on its shaft and not release properly. It really was a high pitched squeal from memory. That was on a 4 speed manual on a car that hadn't been apart for years - the solution was to pull out the starter, strip it down, polish the rust off the shaft where the pinion is supposed to slide freely (it was sticking - not sliding properly) regrease the whole assembly, and put it back together. Four years later it's still going fine. Your problems are more likely to be a mix and match of the wrong components - I've pulled a couple of the short Bosch starters out of 1600 Kents fitted with C3 Auto Trans's at my local wreckers, and also robbed a couple off of Pintos including Cortinas - so I've found the differences.
And yes, the starters all fit up fine using the same bolt pattern.
Beware that there are two different diameter Ring gears used on Escorts and two different types of starters - Lucas or Bosch.
The 1300 & 1600 Kent Engines with manual trans have a smaller diameter ring gear (smaller ring gear, larger starter pinion) to those fitted to the Pintos (which have a larger diameter ring gear and a smaller starter pinion) - and the same applies 1300 + 1600 Kents fitted with C3 Auto trans. The ring gears fitted to Pintos - both manual and automatic - are the same pitch & diameter as those fitted to the 1300 & 1600 Kents with C3 Auto trans.
If you're lucky you will be able to check for burrs & any damage to the ring gear by pulling out the starter motor and having a look in there using a mirror on a stick & a flashlight - be careful using your fingers checking for any burrs on the ring gear as they will be sharp and fingers are soft!
Cheers