About odd pronunciations of "Saturday"

Solution 1:

/ˈsædərˌdeɪ/ > [ˈse˞deʲ]

This isn’t all that uncommon. See the Carpenters’ Saturday, Saturday, ever-lovin’ Saturday!

Merely recite the days of the week as fast as you can starting with Monday, like little kids do, and you always wind up hearing /ˈserdeɪ/, said [ˈse˞ˌdeʲ].

The same sorts of phonological reductions occur in words like bitterly, bladdery, brattery, caterpillar, chattering, clattery, flattery, nattering, rattery and so on, especially under fast-speech rules. It’s just more extreme here.

The normal American pronunciation of Saturday is something you might hear phonemically as /ˈsædərˌdeɪ/, but is actually pronounced more like [ˈsæɾɚˌdeʲ] phonetically.

It then readily loses that first flap because the paired rhotics in [ɾɚ] blend together and leave just a single rhotic.

Phonemic /t/ is never pronounced [t] intervocalically in American, only ever as a coronal flap [ɾ] which is near an denti-alveolar [d], or else as a glottal stop [ʔ]. Both are easily deleted at speed.

Once deleted, that [æ] comes into contact with the [ɹ], at which point the tense–lax distinction between tense [e] and lax [æ] is neutralized just like it is with merry/marry/Mary, leaving you with [eɹ], also written as the r-colored [ e˞].

The final syllable’s /deɪ/ then becomes just [deʲ] or even just [de] spoken quickly in one’s hurry to get to saying Sunday.

Which all boils down to something like [ˈse˞de] with just four spoken sounds.