Moorgate platforms may well have been able to take 5x64 or 6x57 ft cars.
But it is not that simple, and that is not the whole story when 127s were new.
The LM route into Moorgate is very complexicated w.r.t. route restrictions. None of these were set in stone and one must be careful to state any restriction w.r.t. to a time frame. There are height and width and car length restrictions - but not all of them all at the same time or in the same location - some still apply today - but what applies today did not necessarily apply when 127s were new nor when 317s were new - an vice versa. The most difficult section is - and always was - between Kentish Town and what was KX Thameslink. Some of the legacy restrictions have been gradually removed over time, but other works introduced new restrictions also over time.
Going back to the OP question, the Midland route was restricted to 57 ft cars at the time the 127s were introduced new.
It was /something/ like the MR route into Moorgate was limited to 57 ft stock but the GN route via YorkWay / KXSub could take 64 ft stock. That affected DMU types that could be used, as well as short or long frame LH suburban cars. That is why back then on the LM side 127s not to Moorgate but 112/113 could.
Over time there were changes. I /think/ the 57ft restriction was removed around about the time Barbican tracks were slewed and Moorgate rebuilt and enclosed. Since both GN and MR routes had 57 ft LH stock already in place, it did not much affect that LM could now use 64 ft LH stock - but did then allow the 116s in 1970s as mentioned above..
So "A single 4 car set was too short but a double 8 car set was too long" when refering to 127s was not an original issue - 127s were not allowed there outright at that time.
It all comes back to comparing the count of 127s delivered under Bedford dieselisation covered less route and less services than the count of 317s delivered under MSE => not directly comparable.
Digressing, there were other clearance issues. Different stock at different times, and in no particular order :
319s were set lower on suspensions than others of the same type e.g. 321; your ABC Spotting Book Of Numbers will tel you the body dimension are the same, but 319s were set up on the absolute minimum possible - this is for OLE height clearance through the ex-KX TL / today STP area.
The design change from the 317 type body to the 319/321 that introduced the drivers cab plug door was driven by tunnel clearances between Kentish Town and KX TL; the elimination of the 317 end vestibule layout with the driving cabs having no side doors to that of a driving cab with side doors was the high level change - but it was the tunnel clearance detail that led to the exact plug door design used.
313s - despite that a 313 is overall a lower height body (precisely for tunnel work) they were neve allowed on the MR route into Moorgate when they were temporarily used on the Midland, they were limited to the StPancras service.
Today the OLE through STP TL is still an issue, it is the lowest on the route anywhere, and, I have heard it said, is the lowest live 25 kV anywhere on NR running lines.
317s and 319s had end of unit exits - 317s with the full gangway, 319s with the emergency door. 700s do not have these ends doors (they could have had, per 717s, it was not a design blocking point as has been alleged elsewhere). The end emergecny exits was driven by single bore tunnels exceeding a certain length - but those tunnels that drove the 317/319 need were east of Farringdon on the Moorgate line, which closed, so 700s had no requirement for them. The relevant 'single bores' came into place also as part of the Barbican centre works with buildings under pinning. Yes it is obviously true non gangwayed stock and no end of unit egress stock worked the route - but legislaton changes (and accident report recomendations) demanded 317/319 so built; the older legacy stock types were tolerated and/or had exemptions.
Short platforms. 317s and 319s into Moorgate did something Up direction at Barbican that was pure legacy that would never never be allowed these days - Barbican Up was 7car platform but the was no SDO, the rear car was not on the platform, but the doors were released and you could open them. What there was there was a ledge, no way could you call it platform in a passegner sense, that you would more or less have had to have shuffled along sideways to use. I did open the doors on a 319 once to take a look, there is no way I'd have tried to exit there, unless the thing was on fire etc. Barbican Down was only 4car, that was worked around by 8car not stopping there.
And so on.
My main point however is, beware that when stating issues on the Moorgate lines, ensure you state a time frame, and not just "it was X" or "Y was not allowed".
