As far as i understand this thread UA has done a very good job on modelling old Marshalls.
I have quite some experience with NMV and MV amps from the 70s (1959 and 2203/2204 models) and can confirm some of the tipps written above.
Old Marshalls are very sensitive to input gain and thats where the fun comes from imo. They react to the guitars volume knob like an external gain adjustment. If you want clean, you have different option:
1) Adjust the amp for your dirt sound with the guitars` volume on 10 and than simply roll back your guitars volume knob. If the amp has a bright cap, it will retain the sparly highs better.
2) Use a different input on the amp. Both of the low inputs, treble and normal side, are -6db inputs. So every signal coming in doesn`t drive the input stage of the amp that hard and results in less distortion (and less volume). Therefore you get much cleaner sounds while still being freaking loud ... you know 100 Watt Marshalls

For the 2203 Mastervolume amps the same applies. Actually i find the low input on 2203 (2 holer) gives me the nicest cleans of any amp i`ve ever had.
So try to experiment with the inputrouting in the app!
Also the different combinations of patching the inputs does wonders. Here is how i do it on my 76 100 Watter if i want a straight rock tone:
I use a patch cable going from treble input 2 (low) to normal input 1 (high). Than i plug my guitar cable into Treble input 1 (high).
With guitar at volume 9 (smidge below max) i adjust my tone with the volume controls on the amp. i.e. turn treble volume up to 7 for example and than add some missing bass by turning up the normal volume pot to taste. Usually i end up with treble volume at 7 and normal volume between 4 and 6 depending on the guitar. Than i adjust the eq on the amp and most important the presence. Thats how i set up my old 70s Marshalls.
Guitar at volume 8 gives me restrained rock tone for verse, guitarvolume on 9 adds distortion and volume for chorus and on 10 (plus Boss SD1 and delay pedal) gives great solo tones. If i want to go clean i lower the guitar volume by ear, maybe to 3-5.
My post got a bit out of hand but i hope it helps tuning your pedal to your taste.